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Assignment MasteringPhysics: Print View
04/19/2007 02:22 PM
[ Assignment View ]
[ Pri
Elisfri 2, vor 2007
28. Sources of Magnetic Field
Assignment is due at 2:00am on Wednesday, March 7, 2007
Credit for problems submitted late will decrease to 0% after the deadline has passed. The wrong answer penalty is 2% per part. Multiple choice questions are penalized as described in the online help. The unopened hint bonus is 2% per part. You are allowed 4 attempts per
Field from Moving Charges
Magnetic Field near a Moving Charge
A particle with positive charge is moving with speed along the z axis toward positive . At the time of this problem it is located at the origin, . Your task is to find the magnetic field at various locations in the three- dimensional space around the moving charge.
Part A Which of the following expressions gives the magnetic field at the point due to the moving charge?
A. B. C. D.
ANSWER:
Answer not displayed
Part B Find the magnetic field at the point Part B.1 .
Find the magnetic field direction Part not displayed
Express your answer in terms of ANSWER:
, , , and
, and use
, , and
for the three unit vectors.
= Answer not displayed
Part C Find the magnetic field at the point Express your answer in terms of ANSWER: ,,, . , and , and use , , and for the three unit vectors.
= Answer not displayed
Part D Find the magnetic field at the point Part D.1 Evaluate the cross product Part not displayed Part D.2 Find the distance from the charge Part not displayed Express your answer in terms of ,,, , , and , and use , , and for the three unit vectors. .
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ANSWER:
= Answer not displayed
Part E The field found in this problem for a moving charge is the same as the field from a current element of length Hint E.1 Making a correlation Hint not displayed ANSWER: Answer not displayed carrying current provided that the quantity is replaced by which quantity?
Force between Moving Charges
Two point charges, with charges is at ( and , are each moving with speed toward the origin. At the instant shown is at position (0, ) and
, 0). (Note that the signs of the charges are not given because they are not needed to determine the magnitude of the forces
between the charges.)
Part A What is the magnitude of the electric force between the two charges? Hint A.1 Which law to use
Apply Coulomb's law:
where
is the distance between the two charges. Find the value of for the given situation? .
Part A.2
What is the value of
Express your answer in terms of ANSWER: =
Express
in terms of
, =
,
, and
.
ANSWER:
Part B What is the magnitude of the magnetic force on Hint B.1 due to the magnetic field caused by ?
How to approach the problem at the position of charge . Then evaluate the magnetic force on due to the field of .
First, find the magnetic field generated by charge Part B.2
Magnitude of the magnetic field
The Biot - Savart law, which gives the magnetic field produced by a moving charge, can be written , where of is the permeability of free space and is the vector from the charge to the point where the magnetic field is produced. Note we have in the numerator, not , necessitating an extra power
in the denominator. due to charge .
Using this equation find the expression for the magnitude of the magnetic field experienced by charge Part B.2.a Determine the cross product ?
What is the magnitude of For any two vectors,
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, where is the angle between the vectors. Because, in this case, is 45 degrees,
Substitute the appropriate value of Express your answer in terms of ANSWER: =
for this problem, to arrive at a surprisingly simple answer. and .
Note that
is cubed in the denominator of the Biot - Savart law. (at the location of ) in terms of ,, , and .
Express the magnitude of the magnetic field of ANSWER: =
Part B.3
Find the direction of the magnetic field at ? Remember, according to the Biot - Savart law, the field must be perpendicular to both and .
Which of the following best describes the direction of the magnetic field from Ignore the effects of the sign of ANSWER: .
(along the x axis) (along the y axis) (along the z axis into or out of the screen)
Hint B.4
Computing the force
You can evaluate the force exerted on a moving charge by a magnetic field using the Lorentz force law: , where is the force on the moving charge, . Express the magnitude of the magnetic force in terms of ANSWER: = , ,, , and . is the magnetic field, is the charge of the moving charge, and is the velocity of the charge. Note that, as long as and are perpendicular,
Part C Assuming that the charges are moving nonrelativistically ( Hint C.1 How to approach the problem . ), what can you say about the relationship between the magnitudes of the magnetic and electrostatic forces?
Determine which force has a greater magnitude by finding the ratio of the electric force to the magnetic force and then applying the approximation. Recall that ANSWER:
The magnitude of the magnetic force is greater than the magnitude of the electric force. The magnitude of the electric force is greater than the magnitude of the magnetic force. Both forces have the same magnitude.
This result holds quite generally: Magnetic forces between moving charges are much smaller than electric forces as long as the speeds of the charges are nonrelativistic.
Biot - Savart Law: B- Field from Current Elements
Magnetic Field from Current Segments
Learning Goal: To apply the Biot - Savart law to find the magnetic field produced on the z axis from current elements in the xy plane. In this problem you are to find the magnetic field component along the z axis that results from various current elements in the xy plane (i.e., at The field at a point due to a current- carrying wire is given by the Biot - Savart law, , ).
where
and
, and the integral is done over the current- carrying wire. Evaluating the vector integral will typically involve the following steps: , , and . and . Again, finding the cross product can be done either
Choose a convenient coordinate system - - typically rectangular, say with coordinate axes Write in terms of the coordinate variables and directions ( ,
, etc.). To do this, you must find
geometrically (by finding the direction of the cross product vector first, then checking for cancellations from any other portion of the wire, and then finding the magnitude or relevant
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MasteringPhysics: Assignment Print View
component) or algebraically (by using
04/19/2007 02:22 PM
, etc.).
Evaluate the integral for the component(s) of interest. In this problem, you will focus on the second of these steps and find the integrand for several different current elements. You may use either of the two methods suggested for doing this. Part A The field at the point shown in the figure due to a single current element is given by ,
where
and
. In this expression, what is the variable
in terms of
and/or
?
Hint A.1
Making sense of subscripts Hint not displayed
ANSWER:
Part B Find , the z component of the magnetic field at the point from the current flowing over a short distance located at the point .
Hint B.1
Cross product and are parallel?
The key here is the cross product in the Biot - Savart law. What is the cross product when Express your answer in terms of , ANSWER: =0 , , , and
. Recall that a component is a scalar ; do not enter any unit vectors.
Part C Find , the z component of the magnetic field at the point from the current flowing over a short distance located at the point .
Part C.1 What is
Determine the displacement from the current element , the distance (magnitude) from the current element to the point in question ? =
ANSWER:
Part C.2
Find the direction from the cross product
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What is the unit vector that describes the direction of the magnetic field at the origin Express your answer in terms of ANSWER: , , or . ?
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Express your answer in terms of , ANSWER: =
,
,
, and
. Recall that a component is a scalar ; do not enter any unit vectors.
Part D Find , the z component of the magnetic field at the point from the current flowing over a short distance located at the point .
Part D.1
Determine the displacement from the current element Part not displayed
Part D.2
Find the direction of the magnetic field vector ?
What is the unit vector that describes the direction of the magnetic field at the origin Hint D.2.a Evaluating cross products
Hint not displayed Express your answer in terms of ANSWER: , , or .
Express your answer in terms of , ANSWER: =
,
,
, and
. Recall that a component is a scalar ; do not enter any unit vectors.
Part E Find , the z component of the magnetic field at the point P located at from the current flowing over a short distance located at the point .
Part E.1
Determine the displacement from the current element Part not displayed
Part E.2
Use the cross product to get the direction Part not displayed
Express your answer in terms of , ANSWER:
,
,
,
, and
. Recall that a component is a scalar ; do not enter any unit vectors.
=0
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Part F Find , the z component of the magnetic field at the point P located at from the current flowing over a short distance located at the point
04/19/2007 02:22 PM
.
Part F.1 What is
Determine the displacement from the current element , the displacement (magnitude) from the current element to the point in question ? The figure shows another perspective of the same situation to make this calculation easier.
ANSWER:
=
Part F.2
Determine which unit vector to use
Another way to write the Biot - Savart law is ,
where you replace
with
. This eliminates the problem of finding
and can make computation easier. direction. Which component ( , , or ) must you cross with to get a vector in the z direction ? Recall that
You are asked for the z component of the magnetic field. . Express your answer in terms of ANSWER: , , or
points in the
(ignoring the sign).
Part F.3
Evaluate the cross product and the x component of . These two vectors are orthogonal, so finding the cross product is relatively straightforward.
The z component of the magnetic field results from the cross product of What is the value of ? , = , , and .
Give your answer in terms of ANSWER:
Substitute this expression into the formula for the magnetic field given in the last hint. Observe that it has the numerator. Express your answer in terms of , ANSWER: , , , , and
in the denominator since
in the original equation was replaced with
in
. Recall that a component is a scalar ; do not enter any unit vectors.
=
Magnetic Field at the Center of a Wire Loop
A piece of wire is bent to form a circle with radius . It has a steady current flowing through it in a counterclockwise direction as seen from the top (looking in the negative direction).
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Part A What is Part A.1 , the z component of at the center (i.e., ) of the loop ?
Specify the integrand Part not displayed
Part A.2
Perform the integration Part not displayed
Express your answer in terms of , , and constants like ANSWER: = Answer not displayed
and
.
Magnetic Field due to Semicircular Wires
A loop of wire is in the shape of two concentric semicircles as shown. The inner circle has radius ; the outer circle has radius . A current the inner wire. flows clockwise through the outer wire and counterclockwise through
Part A What is the magnitude, Hint A.1 , of the magnetic field at the center of the semicircles ?
What physical principle to use Hint not displayed
Part A.2
Compute the field due to the inner semicircle Part not displayed
Part A.3
Direction of the field due to the inner semicircle Part not displayed
Part A.4
Compute the field due to the straight wire segments Part not displayed
Express
in terms of any or all of the following: , , , and = Answer not displayed
.
ANSWER:
Part B Part not displayed
Force between an Infinitely Long Wire and a Square Loop
A square loop of wire with side length carries a current . The center of the loop is located a distance from an infinite wire carrying a current . The infinite wire and loop are in the same plane; two sides of the square loop are parallel to the wire and two are perpendicular as shown.
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Part A What is the magnitude, Hint A.1 , of the net force on the loop ?
How to approach the problem
You need to find the total force as the sum of the forces on each straight segment of the wire loop. You'll save some work if you think ahead of time about which forces might cancel. Part A.2 Determine the direction of force
Which of the following diagrams correctly indicates the direction of the force on each individual line segment ?
Hint A.2.a
Direction of the magnetic field
In the region of the loop, the magnetic field points into the plane of the paper (by the right - hand rule). Hint A.2.b Formula for the force on a current- carrying conductor with a uniform magnetic field , where is a vector along the wire in the direction of the current. along its length, is
The magnetic force on a straight wire segment of length , carrying a current
b
c
d
Part A.3
Determine the magnitude of force
Which of the following diagrams correctly indicates the relative magnitudes of the forces on the parallel wire segments ?
Part A.3.a
Find the magnetic field due to the wire , of the wire's magnetic field as a function of perpendicular distance from the wire, .
What is the magnitude, Hint A.3.a.i
Ampre's law Hint not displayed
Express the magnetic field magnitude in terms of ANSWER: =
, , and
.
b
c
d
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Part A.4
Find the force on the section of the loop closest to the wire on the section of the loop closest to the wire, that is, a distance from it ?
What is the magnitude of the force Hint A.4.a
Formula for the force on a current- carrying conductor Hint not displayed
Part A.4.b
Find the magnetic field due to the wire Part not displayed
Express your answer in terms of ANSWER: =
,
,
, , and
.
Part A.5
Find the magnetic field due to the wire , of the wire's magnetic field as a function of perpendicular distance from the wire, .
What is the magnitude, Hint A.5.a
Ampre's law Hint not displayed
Express the magnetic field magnitude in terms of ANSWER: , =
, and
.
Express the force in terms of ANSWER: =
,
,,
, and
.
Part B The magnetic moment of a current loop is defined as the vector whose magnitude equals the area of the loop times the magnitude of the current flowing in it ( , of the force on the loop from Part A in terms of the magnitude of its magnetic moment. ), and whose direction is
perpendicular to the plane in which the current flows. Find the magnitude, Express in terms of , = ,, , and .
ANSWER:
The direction of the net force would be reversed if the direction of the current in either the wire or the loop were reversed. The general result is that "like currents" (i.e., currents in the same direction) attract each other (or, more correctly, cause the wires to attract each other), whereas oppositely directed currents repel. Here, since the like currents were closer to each other than the unlike ones, the net force was attractive. The corresponding situation for an electric dipole is shown in the figure below.
Ampere's Law and Examples
Ampres Law Explained
Learning Goal: To understand Ampres law and its application. Ampres law is often written Part A The integral on the left is ANSWER: Answer not displayed .
Part B Part not displayed Part C
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The circle on the integral means that ANSWER:
must be integrated
Answer not displayed
Part D Which of the following choices of path allow you to use Ampres law to find a. The path must pass through the point . is constant along large parts of it. ?
b . The path must have enough symmetry so that c. The path must be a circle. ANSWER: Answer not displayed
Part E Ampres law can be used to find the magnetic field around a straight current- carrying wire. Is this statement true or false ? ANSWER: Answer not displayed
Part F Ampres law can be used to find the magnetic field at the center of a square loop carrying a constant current. Is this statement true or false ? ANSWER: Answer not displayed
Part G Ampres law can be used to find the magnetic field at the center of a circle formed by a current- carrying conductor. Is this statement true or false ? ANSWER: Answer not displayed
Part H Ampres law can be used to find the magnetic field inside a toroid. (A toroid is a doughnut shape wound uniformly with many turns of wire.) Is this statement true or false ? ANSWER: Answer not displayed
Magnetic Field inside a Very Long Solenoid
Learning Goal: To apply Ampre's law to find the magnetic field inside an infinite solenoid. In this problem we will apply Ampre's law, written , to calculate the magnetic field inside a very long solenoid (only a relatively short segment of the solenoid is shown in the pictures). The solenoid has length with each carrying current . It is usual to assume that the component of the current along the z axis is negligible. (This may be assured by winding two layers of closely spaced wires that spiral in opposite directions.) From symmetry considerations it is possible to show that far from the ends of the solenoid, the magnetic field is axial. , diameter , and turns per unit length
Part A Which figure shows the loop that the must be used as the Amprean loop for finding for inside the solenoid ?
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Part A.1
Choice of path for loop integral Part not displayed
ANSWER:
Answer not displayed
Part B Part not displayed Part C Part not displayed Part D Part not displayed Part E Find , the z component of the magnetic field inside the solenoid where Ampre's law applies. , , , , and physical constants such as .
Express your answer in terms of ANSWER:
= Answer not displayed
Part F Part not displayed Part G The magnetic field inside a solenoid can be found exactly using Ampre's law only if the solenoid is infinitely long. Otherwise, the Biot - Savart law must be used to find an exact answer. In practice, the field can be determined with very little error by using Ampre's law, as long as certain conditions hold that make the field similar to that in an infinitely long solenoid. Which of the following conditions must hold to allow you to use Ampre's law to find a good approximation? a. Consider only locations where the distance from the ends is many times b . Consider any location inside the solenoid, as long as c. Consider only locations along the axis of the solenoid. is much larger than . for the solenoid.
Hint G.1
Implications of symmetry Hint not displayed
Hint G.2
Off- axis field dependence Hint not displayed
ANSWER:
Answer not displayed
Magnetic Field of a Current- Carrying Wire
Find the magnetic field a distance Part A First find the magnetic field, , outside the wire (i.e., when the distance is greater than ). from the center of a long wire that has radius and carries a uniform current per unit area in the positive z direction.
Hint A.1
Ampre's law with current density Hint not displayed
Part A.2
Find the direction of the field Part not displayed
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Part A.3
Find the left - hand side of Ampre's law Part not displayed
Part A.4
Find the right - hand side of Ampre's law Part not displayed
Express
in terms of the given parameters, the permeability constant
, the variables ,
(the magnitude of
), , , and , and the corresponding unit vectors , , and . You
may not need all these in your answer. ANSWER: = Answer not displayed
Part B Now find the magnetic field inside the wire (i.e., when the distance is less than ).
Part B.1
Establish the relationiship to Part A Part not displayed
Part B.2
Integrate over the Amprean loop Part not displayed
Express your answer. ANSWER:
in terms of the given parameters, the permeability constant
, the distance
from the center of the wire, and the unit vectors , , and . You may not need all these in
= Answer not displayed
Magnetic Field inside a Toroid
A toroid is a solenoid bent into the shape of a doughnut. It looks similar to a toy Slinky with ends joined to make a circle. Consider a toroid consisting of flowing through it. Consider the toroid to be lying in the r the screen). Let plane of a cylindrical coordinate system, with the z axis along the axis of the toroid (pointing out of be the distance from the axis of the toroid. direction. turns of a single wire with current
represent the angular position around the toroid, and let
For now, treat the toroid as ideal; that is, ignore the component of the current in the
Part A The magnetic field inside the toroid varies as a function of which parameters ? Hint A.1 Consider rotational symmetry
You were asked to assume that the toroid is rotationally symmetric, so its magnetic field cannot depend on . ANSWER:
only only both and
Part B Inside the toroid, in which direction does the magnetic field point? ANSWER: (outward from the center) (inward toward the center)
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(clockwise) (counterclockwise) (out of the screen) (into the screen)
Notice that the
direction is antiparallel to the path shown by the Amprean loop in the figure. Also, by definition,
.
Part C What is Hint C.1 , the magnitude of the magnetic field inside the toroid and at a distance How to approach the problem Hint not displayed Part C.2 Evaluate the line integral Part not displayed Part C.3 Find Part not displayed Express the magnetic field in terms of , ANSWER: = (the permeability of free space), , and . from the axis of the toroid ?
Part D In an ideal toroid, current would flow only in the and directions. The magnetic field in the central plane, outside of the coils of such a toroid, is zero. For the toroid shown in the figures however, direction, and thus the current
this field is not quite zero. This is because in this problem, there is a single wire that is wrapped around a doughnut shape. This wire must point somewhat in the must actually have a component in the Compute direction.
, the magnitude of the magnetic field in the center of the toroid, that is, on the z axis in the plane of the toroid. Assume that the toroid has an overall radius of is large compared to the diameter of the individual turns of the toroid coils.
(the distance from the
center of the toroid to the middle of the wire loops) and that
Note that whether the field points upward or downward depends on the direction of the current, that is, on whether the coil is wound clockwise or counterclockwise. Hint D.1 Simplifying the problem
For this question, it is useful to consider the Biot - Savart law: .
Since the question asks only for the z component of the magnetic field, we need only deal with those portions of that the wire is wrapped in loops of radius is irrelevant; only the component of the current flow in the
that are parallel to
(keeping in mind that
). In other words, the fact
direction is important.
With this simplification, the problem of finding the magnetic field at the center of the toroid becomes equivalent to finding the magnetic field at the center of a single circular loop of wire! Express in terms of , = ,, , and the local diameter of the coils.
ANSWER:
This is the same expression that you would derive for the magnetic field at the center of a circular loop of current- carrying wire. To see why this makes sense, imagine that the local diameter the coils gets so small that it is negligible in comparison to the radius of the toroid. The wire makes one complete turn around the axis of the toroid. So, to a point in the center, the toroid looks like a simple current loop.
of
Current Sheet
Consider an infinite sheet of parallel wires. The sheet lies in the xy plane. A current runs in the - y direction through each wire. There are wires per unit length in the x direction.
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Part A Write an expression for Use , the magnetic field a distance above the xy plane of the sheet.
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for the permeability of free space. How to approach the problem Hint not displayed
Hint A.1
Part A.2
Find Part not displayed
Part A.3
Determine the direction of the magnetic field Part not displayed
Hint A.4
Magnitude of the magnetic field Hint not displayed
Part A.5
Evaluate Part not displayed
Express the magnetic field as a vector in terms of any or all of the following: ANSWER: = Answer not displayed
,,
,,
, and the unit vectors
, , and/or .
Magnetic Fields in Matter
Magnetic Materials
Part A You are given a material which produces no initial magnetic field when in free space. When it is placed in a region of uniform magnetic field, the material produces an additional internal magnetic field parallel to the original field. However, this induced magnetic field disappears when the external field is removed. What type of magnetism does this material exhibit ? ANSWER: diamagnetism paramagnetism ferromagnetism
When a paramagnetic material is placed in a magnetic field, the field helps align the magnetic moments of the atoms. This produces a magnetic field in the material that is parallel to the applied field. Part B Once again, you are given an unknown material that initially generates no magnetic field. When this material is placed in a magnetic field, it produces a strong internal magnetic field, parallel to the external magnetic field. This field is found to remain even after the external magnetic field is removed. Your material is which of the following ? ANSWER: diamagnetic paramagnetic ferromagnetic
Very good! Materials that exhibit a magnetic field even after an external magnetic field is removed are called ferromagnetic materials. Iron and nickel are the most common ferromagnetic elements, but the strongest permanent magnets are made from alloys that contain rare earth elements as well. Part C What type of magnetism is characteristic of most materials? ANSWER: ferromagnetism paramagnetism diamagnetism no magnetism
Almost all materials exhibit diamagnetism to some degree, even materials that also exhibit paramagnetism or ferromagnetism. This is because a magnetic moment can be induced in most common atoms when the atom is placed in a magnetic field. This induced magnetic moment is in a direction opposite to the external magnetic field. The addition of all of these weak magnetic moments gives the material a very weak magnetic field overall. This field disappears when the external magnetic field is removed. The effect of diamagnetism is often masked in paramagnetic or ferromagnetic materials, whose constituent atoms or molecules have permanent magnetic moments and a strong tendency to align in the same direction as the external magnetic field.
Forces between a Charge and a Bar Magnet
Learning Goal: To understand the forces between a bar magnet and 1. a stationary charge, 2. a moving charge, and 3. a ferromagnetic object. A bar magnet oriented along the y axis can rotate about an axis parallel to the z axis. Its north pole initially points along . Interaction of stationary charge and bar magnet A positive charge is displaced some distance in the direction from the magnet.
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Assume that no charges are induced on the magnet.
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Part A Assume that the length of the magnet is much smaller than the separation between it and the charge. As a result of magnetic interaction (i.e., ignore pure Coulomb forces) between the charge and the bar magnet, the magnet will experience which of the following ? ANSWER: Answer not displayed
Interaction of moving charge and bar magnet Consider a second case in which the charge is again some distance in the direction from the magnet, but now it is moving toward the center of the bar magnet, that is, with its velocity along .
Part B Due to its motion in the magnetic field of the bar magnet, the charge will experience a force in which direction ? Part B.1 Determine the magnetic field direction near a charge Part not displayed Part B.2 Determine the direction of force on a charge moving in a magnetic field Part not displayed ANSWER: Answer not displayed
Interaction of iron and bar magnet Now the charge is replaced by an electrically neutral piece of initially unmagnetized soft iron (for example, a nail) that is not moving.
Part C As a result of the magnetic interaction between the soft iron and the bar magnet, which of the following will occur? Hint C.1 Magnetic induction Hint not displayed ANSWER: Answer not displayed
Summary
5 of 13 problems complete (28.67% avg. score) 17.3 of 22 points
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http:/session.masteringphysics.com/myct04/19/2007 05:03 PM[ Assignment View ][ Print ]Elisfri 2, vor 200732. Electromagnetic WavesAssignment is due at 2:00am on Wednesday, March 28, 2007Credit for problems submitted late will decrease to 0% after t

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MasteringPhysics: Assignment Print Viewhttp:/session.masteringphysics.com/myct/assignmentPrint?assig.[ Assignment View ]Elisfri 2, vor 200733. The Nature and Propagation of LightAssignment is due at 2:00am on Wednesday, January 17, 2007Credit for pr

Kettering - MASTERING - PHYS

MasteringPhysics: Assignment Print Viewhttp:/session.masteringphysics.com/myct/assignmentPrint?assig.[ Assignment View ]Elisfri 2, vor 200734. Geometric Optics and Optical InstrumentsAssignment is due at 2:00am on Wednesday, January 17, 2007Credit f

Kettering - MASTERING - PHYS

MasteringPhysics: Assignment Print Viewhttp:/session.masteringphysics.com/myct/assignmentPrint?assig.[ Assignment View ]Elisfri 2, vor 200735. InterferenceAssignment is due at 2:00am on Wednesday, January 17, 2007Credit for problems submitted late w

Kettering - MASTERING - PHYS

MasteringPhysics: Assignment Print Viewhttp:/session.masteringphysics.com/myct/assignmentPrint?assig.[ Assignment View ]Elisfri 2, vor 200736. DiffractionAssignment is due at 2:00am on Wednesday, January 17, 2007Credit for problems submitted late wi

Kettering - MASTERING - PHYS

Chapte 24. Ele r ctric Pote ntial24.1. What is Physics? 24.2. Ele ctric Pote ntial Ene rgy 24.3. Ele ctric Pote ntial 24.4. Equipote ntial S urface s 24.5. C alculating thePote ntial fromtheFie ld 24.6. Pote ntial Dueto a Point C harge 24.7. Pote ntial D

Kettering - MASTERING - PHYS

Electric Potential Electric Potential Energy versus Electric Potential Gravitational Force and Potential Energy First we review the force and potential energy of an object of mass gravitational field that points downward (in the near the earth's surface.

Kettering - MASTERING - PHYS

PHYS-225Homework 225CFall 2009Dr. RussellPart 1: Mean and Uncertainty (6 pts) The data set at right shows a set of data points representing measurements of the electric field at a certain location.1. Enter this data into an Excel spreadsheet. 2. Calc

Kettering - MASTERING - PHYS

23.4. Model: Light rays travel in straight lines. Also, the red and green light bulbs are point sources.Visualize:Solve:The width of the aperture is w = 1 m. From the geometry of the figure for red light,w2 x = x = 2w = 2 (1.0 m ) = 2.0 m 1m 3m + 1mT

Kettering - MASTERING - PHYS

24.40. Model: Assume thin lenses and treat each as a simple magnifier with M = 25cm/f .Visualize: Equation 24.10 gives the magnification of a microscope.M = mobjM eye = L 25cm f obj f eyeSolve: (a) The more powerful lens (4) with the shorter focal len

Kettering - MASTERING - PHYS

22.2. Model: Two closely spaced slits produce a double-slit interference pattern.Visualize: The interference pattern looks like the photograph of Figure 22.3(b). It is symmetrical, with the m = 2 fringes on both sides of and equally distant from the cent

Kettering - MASTERING - PHYS

MasteringPhysics10/19/08 6:50 PMAssignment Display Mode:View Printable Answers[PPhysys 202 Fall08HW4Due at 11:00pm on Wednesday, October 8, 2008View Grading DetailsIntroduction to Electric CurrentDescription: Mostly conceptual questions about el

Kettering - MASTERING - PHYS

26.14. Model: Model the plastic spheres as point charges.Visualize:Solve:(a) The charge q1 = 50.0 nC exerts a force F1 on 2 on q2 = 50.0 nC to the right, and the charge q2 exerts9 2 2 9 9 K q1 q2 ( 9.0 10 N m /C ) ( 50.0 10 C ) ( 50.0 10 C ) = = 0.056

Kettering - MASTERING - PHYS

27.10. Model: The rod is thin, so assume the charge lies along a line. Visualize:Solve: The force on charge q is F = qErod . From Example 27.3, the electric field a distance r from the center of a charged rod isErod = Thus, the force is1Q4 0 r r 2 +

Kettering - MASTERING - PHYS

28.4. Model: The electric flux flows out of a closed surface around a region of space containing a netpositive charge and into a closed surface surrounding a net negative charge. Visualize: Please refer to Figure EX28.4. Let A be the area in m2 of each o

Kettering - MASTERING - PHYS

29.28. Model: The electric potential at the dot is the sum of the potentials due to each charge.Visualize: Please refer to Figure EX29.28. Solve: The electric potential at the dot isV=1 q1 1 q2 1 q3 + + 4 0 r1 4 0 r2 4 0 r3 5.0 109 C 5.0 109 C q = ( 9

Kettering - MASTERING - PHYS

MasteringPhysics5/10/09 3:33 PMAssignment Display Mode:View Printable Answers[ Print ]phy260S09HW9Due at 11:00pm on Thursday, April 16, 2009View Grading DetailsCharged Aluminum SpheresDescription: Find the number of electrons in an aluminum sphe

Kettering - MASTERING - PHYS

MasteringPhysics5/10/09 3:36 PMAssignment Display Mode:View Printable Answers[ Print ]phy260S09HW10Due at 11:00pm on Tuesday, April 28, 2009View Grading DetailsCharged RingDescription: Find the electric field from a uniformly charged ring (quali

Kettering - MASTERING - PHYS

MasteringPhysics5/10/09 3:39 PMAssignment Display Mode:View Printable Answers[ Print ]phy260S09HW11Due at 11:00pm on Tuesday, May 5, 2009View Grading DetailsEnergy Stored in a Charge ConfigurationDescription: Find the work required to assemble f

Kettering - MASTERING - PHYS

MasteringPhysics5/10/09 3:42 PMAssignment Display Mode:View Printable Answers[ Print ]phy260S09HW12Due at 11:00pm on Tuesday, May 12, 2009View Grading DetailsCapacitors in SeriesDescription: Contains several questions that help practice basic ca

Kettering - MASTERING - PHYS

MasteringPhysics5/10/09 3:55 PMAssignment Display Mode:View Printable Answersphy260S09HW13Due at 12:00am on Monday, June 1, 2009View Grading DetailsHeating a Water BathDescription: Calculate the time required for a resistor to heat a water bath t

Ohio State - BUSFIN - 600

MID TERM ESSAY QUESTIONS A. Variable life insurance has the premiums invested in separate accounts and the face value may increase if the investment results are favorable. Prospects are those who desire life insurance at a fixed, level premium but want to

Ohio State - BUSFIN - 600

BF 640 AUTUMN 2008 FINAL MULTIPLE CHOICE EXAM INSTRUCTOR: CHARLES A. BRYAN NAME: _ Place your answer on the answer sheet and turn the answer sheet in. You may keep the exam. Answers will be posted on Carmen within three days. 1. Risk can be defined as a.

Ohio State - BUSFIN - 600

BF 640 AUTUMN 2008 MID TERM EXAM MULTIPLE CHOICE QUESTIONS ANSWER SHEET NAME: _ Place your answer on the answer sheet and turn the answer sheet in. You may keep the exam. Answers will be posted on Carmen. 1. Risk can be defined as a. Uncertainty concernin

Indiana - MATH - 311

University of Alaska Southeast - CIS - 29977

Fall 2003 Hulstein & Hulstein Intermediate Accounting Chapter # 9 Quiz B Name _1. Designated market value a. is always the middle value of replacement cost, net realizable value, and net realizable value less a normal profit margin. b. should always be e

U. Houston - ASSEMBLY - 0356

Laboratory Short CourseIntroduction to CodeWarrior Running Assembly Programs on the Microcontrollerwww.freescale.com/universityprogramsFreescale and the Freescale logo are trademarks of Freescale Semiconductor, Inc. All other product or service names a

Clarkson - ES - 220

Clarkson - ES - 220

Clarkson - ES - 220

Clarkson - ES - 220

Clarkson - ES - 220

Clarkson - ES - 220

Clarkson - ES - 220

Clarkson - ES - 220

Clarkson - ES - 220

Clarkson - ES - 220

Clarkson - ES - 220

Clarkson - ES - 220

Academy of Art University - ARTS - arts 101

Note that the following lectures include animations and PowerPoint effects such as fly ins and transitions that require you to be in PowerPoint's Slide Show mode (presentation mode).Chapter 4The Origin of Modern AstronomyGuidepostThe sun, moon, and pl

DeAnza College - ARTS - arts 101

Review question from chapter 1:3, What is the difference between our solar system, our galaxy a nd the universe? Our solar system is made up of the Sun (the nearest star), and bodies (like the planets) which are gravitationally bound to it. It is much sm

New York College of Podiatric Medicine - AUD - 5721

1Chapter 1 Introduction to Federal Taxation and Understanding the Federal Tax LawSUMMARY OF CHAPTERThis chapter presents information on the magnitude of federal taxes collected and on taxpayer obligations. Also, the history of U.S. federal taxation is

New York College of Podiatric Medicine - ACT - 3243

9Chapter 2 Tax Research, Practice, and ProcedureSUMMARY OF CHAPTERTax practice involves the preparation of tax returns and representation of clients before the audit or appellate divisions of the Internal Revenue Service. To become a competent professi

Cornell - HADM - 3301

Challenge1 Afterrunningchallenge1withandwithoutbatching,itbecameimmediatelyclearthatBenihana mustusebatchingtoproducethemostprofitableresults.Inoursimulationwithbatchingthe averageprofitwas360.00.Withoutbatchingprofitwasintheredat139.00.Fromthetableyou ca

Cornell - H ADM - 301

The only way to address the bottleneck issue is to get another oven. Kristen has two options, she can either rent an oven from her neighbor or buy another one. If she were to rent another oven, the process would change. Kristen would have to run back and

Cornell - H ADM - 3387

HADM 387 9/16/08 Sexual HarassmentThe original title VII did not include sex so you could technically exclude women from your restaurant There is very little history on sex in the title 1986 Sex.H starts under federal law. Bill passed by congress added

Lawson State - BUSINESS - Acct113

Quiz 4 (20 points) 1. Which of the following circumstances creates a future taxable amount? A. Service fees collected in advance from customers: taxable when received, recognized for f inancial reporting when earned. B. Accrued compensation costs for futu

University of Texas - M - M408K

Frameset OverviewThe Blackboard Learn environment includes a header frame with images and buttons customized by the institution and tabs that navigate to different areas within Blackboard Learn. Clicking on a tab will open that area in the content frame.

University of Texas - M - M408K

Frameset OverviewThe Blackboard Learn environment includes a header frame with images and buttons customized by the institution and tabs that navigate to different areas within Blackboard Learn. Clicking on a tab will open that area in the content frame.

University of Texas - M - M408K

amaefule (bca357) HW02 Gilbert (57195) This print-out should have 13 questions. Multiple-choice questions may continue on the next column or page nd all choices before answering. 001 10.0 points1t (seconds) 0 1 2 3 4 5 s (feet) 0 20 28 36 50 62 Find the

Minnesota - BIOLOGY - A&P

BIOL 237 Case History 1 A 27 year old man, who works outdoors, notices a growth on the skin which includes a darkly pigmented spot surrounded by a halo of inflamed skin. This man has a very fair complexion, with numerous freckles and blond hair. Because o

Minnesota - BIOLOGY - A&P

Angelo Crespin 09/09/09 237.001Connective Tissue HistologyTissue TypeCharacteristics 1. Well Vascularized 2. Contains fibers, cell types, ground substances 3. Most abundant connective tissueFunctionsLocationsAreolar1. Contain Blood, vessels, and ne

Minnesota - BIOLOGY - A&P

Angelo Crespin 09/09/09 237.001 Epithelial Tissue HistologyTissue TypeCharacteristicsFunctions 1. Thinnest tissue in the body. 2. Forms semipermeable membrane in lungs and capillaries. 3. Secretes serous fluid in serous membrane. 1. Goblet cells secret

Minnesota - BIOLOGY - A&P

Epithelial Tissue Histology - Template Tissue Type Simple Squamous Epithelium Characteristics Single Layered Thin and Flat Functions 1. Thinnest tissue in the body. 2. Forms semipermeable membrane in lungs and capillaries. 3. Secretes serous fluid in sero

Minnesota - BIOLOGY - A&P

Angelo Crespin 10/30.09 Biology 237.001Stimulus-Contracting Coupling1) An impulse arrives at the axon terminus generating an action potential which is propagated along the sarcolemma and down the T tubules 2) Next, the action potential triggers Ca2+ rel

Minnesota - BIOLOGY - A&P

Angelo Crespin 09/16/09 Biology 237.001The Skin Match the number of each structure in the skin diagram with its name on the chart, then describe the characteristics or functions of each. The first one has been done as an example.Epidermis Dermis Sebaceo

Purdue - PHYS - PHYS 172

IMPORTANT: Fill in the circle A after TEST FORM under your signature on the answer sheet. PHYS 172 Fall 2008 Wednesday, October 22 EXAM 1 - TEST FORM A There are two parts to Exam 1: the machine-graded part of this test, and the last page that you turn in

Purdue - PHYS - PHYS 172

Two small objects each of mass m are connected by a lightweight rod of length L. At a particular instant they have velocities as shown and are subjected to external forces as shown. The system is moving in outer space.In the following questions involving