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MasteringPhysics
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phy260S09
HW10
Due at 11:00pm on Tuesday, April 28, 2009
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Charged Ring
Description:
Find the electric field from a uniformly charged ring (qualitative and quantitative parts) at points along its axis.
Then use this to find the frequency of small oscillations of a oppositely charged object placed on the axis.
Consider a uniformly charged ring in the
xy
plane, centered at the origin. The ring has radius
and positive charge
distributed
evenly along its circumference.
Part A
What is the direction of the electric field at any point on the
z
axis?
Hint A.1
How to approach the problem
Approach 1
In what direction is the field due to a point on the ring? Add to this the field from a point on the opposite side of the ring. In
what direction is the net field? What if you did this for every pair of points on opposite sides of the ring?
Approach 2
Consider a general electric field at a point on the
z
axis, i.e., one that has a
z
component as well as a component in the
xy
plane. Now imagine that you make a copy of the ring and rotate this copy about its axis. As a result of the rotation, the
component of the electric field in the
xy
plane will rotate also. Now you ask a friend to look at both rings. Your friend
wouldn't be able to tell them apart, because the ring that is rotated looks just like the one that isn't. However, they have the
component of the electric field in the
xy
plane pointing in different directions! This apparent contradiction can be resolved if
this component of the field has a particular value. What is this value?
Does a similar argument hold for the
z
component of the field?
ANSWER:
parallel to the
x
axis
parallel to the
y
axis
parallel to the
z
axis
in a circle parallel to the
xy
plane
Part B
What is the magnitude of the electric field along the positive
z
axis?
Hint B.1
Formula for the electric field
You can always use Coulomb's law,
, to find the electric field (the Coulomb force per unit charge) due to a point
charge. Given the force, the electric field say at
due to
is
.
In the situation below, you should use Coulomb's law to find the contribution
to the electric field at the point
from a piece of charge
on the ring at a distance
away. Then, you can integrate over the ring to find the value of
.
Consider an infinitesimal piece of the ring with charge
. Use Coulomb's law to write the magnitude of the infinitesimal
at a point on the positive
z
axis due to the charge
shown in the figure.
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5/10/09 3:36 PM
MasteringPhysics
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http://session.masteringphysics.com/myct
Use
in your answer, where
. You may also use some or all of the variables
,
, and
.
ANSWER:
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This note was uploaded on 11/02/2009 for the course MASTERING PHYS taught by Professor All during the Spring '09 term at Kettering.
 Spring '09
 All

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