HW-2
1. (a) Let F1 x 2 z and F2 xx yy zz . Calculate the divergence of and curl of F1 and
F2 Which one can be written as the gradient of a scalar? Find a scalar that does the
job. Which one can be wri
Physics 110A
Discussion Section Set 2
Spring 2017
(1) (Griffiths 1.64) This is problem to convince yourselves that 2 (1/r) = 4 3 (r). Consider
the function,
1
1
D(r, ) = 2
4
r2 + 2
(a) Show that D(r,
Physics 110A
Discussion Section Set 4
Spring 2017
(1) (Griffiths 2.35) Here is a fourth way of computing the energy of a uniformly charged solid
sphere: Assemble it like a snowball, layer by layer, ea
Physics 110A Spring 2017
Week 13
Problems
(1) A long straight wire and a small rectangular wire loop lie in the same plane. Determine the
mutual inductance in terms of `1 , `2 , and w. Assume the wire
Physics 110A Spring 2017
Week 1
GSI: Pratik Sachdeva
Problems
(1) Vectors Grab Bag.
(a) Consider two vectors u = (1, 2, 1), v = (2, 4, 5), and w = (4, 9, 2). Evaluate u + v, u v,
u v, and u (v w).
(b)
Physics 110A Spring 2017
Week 9
GSI: Pratik Sachdeva
Problems
(1) A steady current I flows down a long cylindrical wire of radius a. Find the magnetic field,
both inside and outside the wire, if
(a) T
Physics 110A Spring 2017
Midterm II Practice Problems
Midterm II Practice Problems
(1) A thick spherical shell (inner radius a, outer radius b) is made of dielectric material with a
frozen-in polariza
Physics 110A Spring 2017
Week 1
GSI: Pratik Sachdeva
Problems
(1) A hollow spherical shell carries charge density = k/r2 in the region a r b. Find the
electric field in the three regions: (i) r < a, (
Physics 110A
Practice Problem Set Midterm 1 Solutions
Spring 2017
(1) A cubical box (sides of length a) consists of five metal plates, which are welded together and
grounded. The top is made of a sepa
Physics 110A Spring 2017
Week 5
GSI: Pratik Sachdeva
Problems
(1) A point charge q is situated a distance a from the center of a grounded conducting sphere of
radius R. Find the potential outside the
Discussion Section Week 8
Physics 110A
Spring 2017
(1) (Griffiths 4.22) A very long cylinder of linear dielectric material is placed in an otherwise
uniform electric field E 0 . Find the resulting fie
Physics 110A
Discussion Section Week 10
Spring 2017
(1) (Griffiths 6.12) An infinitely long cylinder, of radius R, carries a frozen in magnetization
parallel to the axis,
M = ks
z
where k is a constan
Physics 110A Spring 2017
Final Study Guide
You are responsible for all material in Chapters 1-7 and Sections 9.1, 9.2, and 12.3.
This study guide certainly does not encompass all of that material, so
Physics 110A Spring 2017
Week 7
GSI: Pratik Sachdeva
Problems
(1) A dielectric cube of side a, centered at the origin, carries a frozen-in polarization P = kr,
where k is a constant. Find all the boun
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) D
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
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
HW-10
7.3
1. (a) Two metal objects are embedded in weakly conducting material of conductivity . Show
that the resistance between them is related to the capacitance of the arrangement by
R
0
C
(b) Supp
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.
Solution:
(a) At the sur
Physics 110A, Electromagnetism and Optics
Final Exam
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 evalua
Physics 110A
Problem Set 9 Solutions
Spring 2017
(1) An iron ring of radius 10 cm and of cross-sectional area 12 cm2 is evenly wound with 1200
turns of insulated wire. There is an air gap in the ring
Physics 110A
Problem Set 8 Solutions
Spring 2017
(1) The integral form of Amperes Law, including the displacement term, is given by
Z
Z
Z
E
B d` = 0 J da + 0 0
da.
S t
S
C
(1)
In this case, C is a pa
Physics 110A, Electromagnetism and Optics
Midterm #2
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 evalua
Problem Set 10 Solutions
Physics 110A
Spring 2017
(1) Let us assume that a voltage V is applied between the inner and the outer surface and this
I
causes a current I to flow through the wire. This mea
Problem Set 8 Solutions
Physics 110A
Spring 2017
(1) (a) The vector potential A must produce a valid magnetic field B. The magnetic field B,
under magnetostatics, must have a vanishing divergence i.e.
Physics 110A
Practice Problem Set Midterm 1
Spring 2017
(1) A cubical box (sides of length a) consists of five metal plates, which are welded together and
grounded. The top is made of a separate sheet