HW-1 solution
1. For the two vectors A x 2 y z and B 2 x 3 y z , find (a) A B and A B , (b)
component of B along A , (c) angle between A and B , (d) A B , (e) A B A B .
Solution:
(a) A B ( x 2 y z ) (2 x 3 y z ) 3x y 2 z
| A B | 32 (1) 2 (2) 2 3.74
A 1 (
110 A MIDTERM REVIEW PROBLEMS
SPRING 2008
I am not the one writing the midterm, so these problems may not be representative of the exam. They are probably harder than exam problems would be. There are hints on the second page, if you need them. It i
University of California, Berkeley
Physics 110A Fall 2001 Section 1 (Strovink)
Problem Set 2
1. Griths 2.18
everywhere within the outer sphere. Construct
a Gaussian surface consisting of a third sphere
at radius r, where R1 < r < R2 . Consider the
volume
University of California, Berkeley
Physics 110A Fall 2001 Section 1 (Strovink )
Solution Set 6 (compiled by Daniel Larson)
1. Griths 5.24 If B is uniform, then it is not a function of position, so any derivative of it vanish. In particular,
B = 0 and B =
University of California, Berkeley
Physics 110A Fall 2001 Section 1 (Strovink )
Solution Set 7 (compiled by Daniel Larson)
1. Griths 6.17 In a linear material, we know H is proportional to B: B = H = 0 (1 + m )H, so for a long
wire it should be circumfere
University of California, Berkeley
Physics 110A Fall 2001 Section 1 (Strovink )
Solution Set 11 (by Daniel Larson)
1. Polarization
(a) We want to convert the real electric eld E into a complex electric eld.
E = E0 Re ei(kzt) x + E0 bRe ei(kzt+) y = Re E0
University of California, Berkeley
Physics 110A Fall 2001 Section 1 (Strovink )
Solution Set 10 (compiled by Daniel Larson)
1. Griths 9.19
(a) For a poor conductor,
, we can expand the second square root in the formula for (Eqn 9.126):
1+
2
1+
1
2
2
+ .
University of California, Berkeley
Physics 110A Fall 2001 Section 1 (Strovink)
SOLUTION TO MIDTERM EXAMINATION 1
Directions: Do all 3 problems, which have unequal weight. This is a closed-book closed-note exam
except for one 8 1 11 inch sheet containing a
University of California, Berkeley
Physics 110A Fall 2001 Section 1 (Strovink )
Solution Set 8 (compiled by Daniel Larson)
1. Griths 7.21 The emf is the time-derivative of the ux due to the small loop that passes through the big
loop, namely E = d = M dI
University of California, Berkeley
Physics 110A Fall 2001 Section 1 (Strovink )
Solution Set 3 (compiled by Daniel Larson)
1. Griths 3.1 We want to calculate the average potential on the surface of a sphere due to a point charge q
located somewhere within
University of California, Berkeley
Physics 110A Fall 2001 Section 1 (Strovink )
Solution Set 4 (compiled by Daniel Larson)
1. Griths 3.33 To get a general formula for the electric eld from an electric dipole, lets start with the general
formula for the po
Physics 110A, Electromagnetism and Optics
Discussion Section Problems, Set #1
1. Consider an n-sided polygon with point charges of magnitude q placed at each vertex. Prove
that the electric eld is zero in the center of the polygon.
2. A rod of length L ca
Physics 110A, Electromagnetism and Optics
Homework #3
Due at 5:30 PM on Friday, February 12. Turn in to the designated homework box in LeConte 251.
Reading: Griths, Sections 1.5 - 1.6, 2.2 - 2.3
Homework:
1. Consider a point charge q positioned at the ori
Physics, 110A, Electromagnetism and Optics
Homework #2
Due by 5:30 PM on Friday, February 5. Turn in to the designated homework box in LeConte 251.
Reading: Griths, Sections 1.4 1.6, 2.2 2.3
Homework:
1. Prove, using index notation or otherwise, the follo
Homework #4
1. A metal sphere of radius R, carrying charge q, is surrounded by a thick concentric
metal shell (inner radius a, outer radius b). The shell carries no net charge.
(a) Find the surface charge density at R, at a, and at b.
(b) Find the potenti
Homework #4
1. A metal sphere of radius R, carrying charge q, is surrounded by a thick concentric
metal shell (inner radius a, outer radius b). The shell carries no net charge.
(a) Find the surface charge density at R, at a, and at b.
(b) Find the potenti
HW-3
1. Find the electric field a distance z above the center of circular disk of radius R which
carries a uniform surface charge density . What does your formula give in the limit
R and R < z .
Solution:
Obviously the electric field is in the z direction
University of California, Berkeley
Physics 110A Fall 2001 Section 1 (Strovink )
Solution Set 1
1. Griths 1.14 Under a rotation, the coordinates y and z transform into y = y cos + z sin and z =
y sin + z cos , so we can invert these equations to nd y = y c
University of California, Berkeley
Physics 110A Fall 2001 Section 1 (Strovink )
Solution Set 5 (compiled by Daniel Larson)
1. Griths 5.1 Since the eld is pointing into the page, a positive charge would feel a force in the direction
v B, which is up. So th
University of California, Berkeley
Physics 110A Fall 2001 Section 1 (Strovink )
Solution Set 9 (compiled by Daniel Larson)
qt
1
r
r
1. Griths 10.3 First well calculate the elds. E = V A = 0 4 0 r12 . B = A = 4 0 r = 0.
2
t
These elds should be familiar, b
Physics 110A, Electromagnetism and Optics
Midterm #1
Please read the questions carefully and show all work. You are allowed to use your own notes. If you
find a root or fraction that you cannot evaluate, either estimate it or leave it unsimplified. There
110 A MIDTERM REVIEW SOLUTIONS
SPRING 2008
1 (a) Just invert the answers for a charge outside a grounded sphere. The formulas have the same form: for a charge q a distance a from a sphere of radius R, the image charge has charge and position Q=- qR
PHYSICS 110A Spring 2008 Class Time: T Th 9:30-11 in 160 Dwinelle Hall Instructor: Prof. Mike Crommie. Office: 345 Birge. Phone: 642-9392 email: [email protected] Office hours: T Th 11-12 (or by appt.) TA: Ben Lipshitz. Office: 465 Birge. Phone T
HW-5 1. For a point charge q at a distance a from a spherical conductor of radius R (R<a), we obtained in the lecture the result of the image charge inside the conductor. Starting from that result, calculate the following quantities. (a) The surface charg
HW-6 1. A rectangular pipe, running parallel to the z axis (from - to +), has three ground metal sides at y=0, y=a, and x=0. The fourth side, at x=b, is maintained at a specific potential V0(y). (a) Develop a general formula for the potential within the p
HW-7
P(r ) kr , where k is a constant. 1. A sphere of radius R carries a polarization
(a) Calculate the bound charge b and b. (b) Find the field inside and outside the sphere. 2. The space between the plate a parallel-plate capacitor is filled with two s
HW-8 1. Find the magnetic field at point P for each of the following steady current configurations.
2. Find the force on a square loop and a triangle near in infinite straight wire.
J Jx . 3. A thick slab extending from z=-a to z=+a carries a uniform vol
HW-8 1. Find the magnetic field at point P for each of the following steady current configurations.
Solution: (a) The magnetic field at P are contributed by the current from 4 segments. But the dl r 0 so they do not contribute to two segments in the radia
Physics 137A Midterm #2
Fall 2009 Monday Nov. 16th
1. (25 points) In each case choose the correct statement: (a) In a region of space where the energy eigenvalue E > V (x), the eigenfunction (x) is (i) concave towards the x-axis. (ii) concave away from th