Physics 1B Sixth Week
Class Notes Spring 2010
Walter Gekelman Electrical Potential
Finally let us do back to a ring of charge. We derived an equation for the electric field 1 Qx along the x axis of the ring Ex = Let us 3 . The ring is in the x-z plane. 4

The Right Hand Rule:
The Vector Product:
The rst, and for many, only exposure to the right-hand-rule comes by way of the vector- (or cross-) product, so lets start there.
C A
B
Consider the relationship C = A B (shown graphically in the gure above). |C |

Sound General: Sound propagates as a longitudinal traveling wave - everything weve learned about traveling waves still applies. While you can write the equation for a traveling sound wave in terms of the longitudinal displacement of particles in the media

Displacement of Functions:
The top plot shows a function f (x) which peaks when its argument (x) equals b. In the bottom plot, Ive plotted the same function f , but now every occurance of the the variable x has been replaced with the quantity x a. Since t

Useful Trig Identities
1) sin(A + B ) = sin A cos B + sin B cos A 2) sin(A B ) = sin A cos B sin B cos A 3) cos(A + B ) = cos A cos B sin A sin B 4) cos(A B ) = cos A cos B + sin A sin B
The following identities can be derived from the above identities,

MTl Physics 1B, 810
Full Name (rememﬂ
Full Name (Signaturﬂ
Student ID Number MM
Seat Number
- Do not peek at the exam until you are told to begin. You will have approximately 50 minutes
to complete the exam.
0 Don’t spend too much time on any one proble

CHAPTER
14
SUMMARY
1
T
Periodic motion: Periodic motion is motion that repeats
itself in a definite cycle. It occurs whenever a body has a
stable equilibrium position and a restoring force that
acts when it is displaced from equilibrium. Period T is
the t

462
CHAPTER 14 Periodic Motion
Damped oscillations: When a force Fx = -bvx proportional to velocity is added to a simple harmonic oscillator, the motion is called a damped oscillation. If
b 6 2 2km (called underdamping), the system oscillates with a decay

CHAPTER
22
SUMMARY
Electric flux: Electric flux is a measure of the flow of
electric field through a surface. It is equal to the product
of
an area element and the perpendicular component of
S
E, integrated over a surface. (See Examples 22.122.3.)
E =
L
E

CHAPTER
21
SUMMARY
Electric charge, conductors, and insulators: The fundamental quantity in electrostatics is electric
charge. There are two kinds of charge, positive and negative. Charges of the same sign repel each
other; charges of opposite sign attrac

CHAPTER
24
SUMMARY
Capacitors and capacitance: A capacitor is any pair of
conductors separated by an insulating material. When
the capacitor is charged, there are charges of equal magnitude Q and opposite sign on the two conductors, and
the potential Vab

CHAPTER
23
SUMMARY
Electric potential energy: The electric force caused by
any collection of charges at rest is a conservative force.
The work W done by the electric force on a charged particle moving in an electric field can be represented by
the change

CHAPTER
25
SUMMARY
Current and current density: Current is the amount of
charge flowing through a specified area, per unit time.
The SI unit of current is the ampere 11 A = 1 C>s2. The
current I through an area A depends on the concentration n and charge

CHAPTER
27
SUMMARY
Magnetic forces: Magnetic interactions are fundamentally interactions between moving charged particles.
These interactionsSare described by the vector magnetic
field, denoted by B. A particle with Scharge q moving
S
with
velocity v in a

Physics 1B Walter Gekelman Capacitors and Capacitance
Class Notes
Week 7
Consider the potential on axis of a ring of charge (1) V =
1 4 0
Q x 2 + a2
. X is the distance from the center
For a line of charge with charge density (chg/length) , and length 2a,

Physics 1 B Class Notes Walter Gekelman
Spring Quarter 2010 DC Circuits Week 9
Consider an RC circuit containing a capacitor a resistor and a battery. What happens when you close the switch?
S E C
R
Assume the current is counterclockwise and use Kirchoffs

Physics 1B Magnetism
Class Notes Walter Gekelman Week 10
We have studies the force law for a charge in an electric field F = qE . If a magnetic field is present the generalized law, called the Lorentz equation is:
(1) F = q E + v B
(
)
The magnetic fiel

Damped Harmonic Motion Closing Doors and Bumpy Rides
Andrew Forrester May 4, 2010
Prerequisites and Goal
Assuming you are familiar with simple harmonic motion, its equation of motion, and its solutions, we will now proceed to damped harmonic motion. In th

Physics 1B: E-Field from a Point-Source Integral E-Field of a Plane of Charge 1 Problem
Using the remote-point-source expression for the electric eld (rather than Gausss law), solve for the electric eld everywhere surrounding an innite plane with surface

V k M DAMPER
kx
bv
Damped Oscillators
Consider the system pictured above. It looks like a normal mass on a spring conguration, except for the motion damper (of drag constant b) attached to the right side of the apparatus. Fx = max d2 x kx bvx = m 2 dt d2

DRIVER k M kx ( F0 Cos t + ) bv DAMPER
Driven Oscillators
Consider the system pictured above. A damped oscillating system is attached to a motorized contraption that exerts an oscillating force of amplitude F0 at an angular frequency . The phase of the co

k m kx
Free Oscillators:
Consider the simple system shown above. Use the force method to nd its equation of motion.
Fx = max d2 x kx = m 2 dt d2 x k 0= +x 2 dt m Since we know this thing is going to oscillate (move back and forth in a periodic manner) let

Taylors Theorem
If you look up Taylors theorem in any decent calculus book, it will tell you that you can take any function and express it as a sum of polynomial terms. You can use Taylors theorem to nd alternative ways of calculating transcendental funct