Assignment 1 Solution
1.
(a) Direction: perpendicular to the contour line and pointing in the direction of
increasing H.
Relative magnitude: Gradient at a should have greater magnitude than that
at b.
(b) Print the figure on A4 paper. Use a ruler to estim

Assignment 8 Solution
Problem 1.
Problem 2.
Choose coordinates such that both dipoles point towards +x direction. Put m1
and m 2 at ( x, y, z ) = (0, 0, 0) and (r , 0, 0) respectively, the force acting by
m1 on m 2 is
F12 = ( m 2 B1 )
3
= m 2 0 3 2 ( m1

PHYS 3033 Assignment 6
Due: 25 Oct 2013 at begin of lecture at 4:30 pm
Problem 1.
A thick spherical shell (inner radius a, outer radius b) is made of the dielectric material with a
frozen-in polarization
k
r
r
P (r ) =
where k is a constant and r is the d

PHYS 3033 Assignment 4
Due: 11 Oct 2013 at begin of lecture at 4:30 pm
Problem 1.
Show that in general the average potential over a spherical surface of radius R is
Q
Vave = Vcenter + enc ,
4 0 R
where Vcenter is the potential at the center due to all the

PHYS 3033 Assignment 5
Due: 18 Oct 2013 at begin of lecture at 4:30 pm
Problem 1.
Consider a spherical shell of Radius R. There is vacuum, with no charges, both inside and
outside the shell. A surface charge density ( ) = 0 (3cos2 -1) is glued to the surf

PHYS 3033 Assignment 2
Due: 25 Sept 2013 at begin of lecture at 4:30 pm
Problem 1.
a) Ten equal charges, q, are situated at the corners of a regular 10-sided polygon. What is the net
force on a test charge Q at the center?
b) Suppose one of the 10 qs is r

PHYS 3033 Assignment 8
Due: 15 Nov 2013 at begin of lecture at 4:30 pm
Problem 1.
Consider an infinitesimal square of side . Choose the coordinate system such that the square is
in the first quadrant on the yz plane, with one corner at the origin and side

PHYS 3033 Assignment 3
Due: 2 Oct 2013 at begin of lecture at 4:30 pm
Problem 1.
A sphere of radius R carries a charge density ( r ) = kr 2 (where k is a constant). Find the energy
of the configuration using
W=
(a)
W=
(b)
0
2
E 2 d ,
all space
1
Vd .
2
Pr

PHYS 3033 Assignment 7
Due: 8 Nov 2013 at begin of lecture at 4:30 pm
Problem 1.
A point charge q is imbedded at the center of a sphere of linear dielectric material (with
susceptibility e and radius R). Find the electric field, the polarization, and the

PHYS 3033 Assignment 6
Due: 25 Oct 2013 at begin of lecture at 4:30 pm
Problem 1.
A thick spherical shell (inner radius a, outer radius b) is made of the dielectric material with a
frozen-in polarization
k
r
r
P (r ) =
where k is a constant and r is the d

PHYS 3033 Assignment 10
Due: 29 Nov 2013 at begin of lecture at 4:30 pm
Problem 1.
A wire of the shape of a regular hexagon with side length s and carrying uniform current I flowing in the
counterclockwise direction has its right half inside a uniform mag

PHYS 3033 Assignment 4
Due: 11 Oct 2013 at begin of lecture at 4:30 pm
Problem 1.
Show that in general the average potential over a spherical surface of radius R is
Q
Vave = Vcenter + enc ,
4 0 R
where Vcenter is the potential at the center due to all the

PHYS 3033 Assignment 2
Due: 25 Sept 2013 at begin of lecture at 4:30 pm
Problem 1.
a) Ten equal charges, q, are situated at the corners of a regular 10-sided polygon. What is the net
force on a test charge Q at the center?
b) Suppose one of the 10 qs is r

PHYS 3033 Assignment 7
Due: 8 Nov 2013 at begin of lecture at 4:30 pm
Problem 1.
A point charge q is imbedded at the center of a sphere of linear dielectric material (with
susceptibility e and radius R). Find the electric field, the polarization, and the

PHYS 3033 Assignment 1
Due: 13 Sep 2013 at begin of lecture at 4:30 pm
1.
(a) The figure below is the contour plot of the height (H) of a mountain on the
horizontal (xy) plane. Sketch the gradients H at point a and point b. Pay
attention to both the corre

PHYS 3033 Assignment 10
Due: 29 Nov 2013 at begin of lecture at 4:30 pm
Problem 1.
A wire of the shape of a regular hexagon with side length s and carrying uniform current I flowing in the
counterclockwise direction has its right half inside a uniform mag

PHYS 3033 Assignment 3
Due: 2 Oct 2013 at begin of lecture at 4:30 pm
Problem 1.
A sphere of radius R carries a charge density ( r ) = kr 2 (where k is a constant). Find the energy
of the configuration using
W=
(a)
W=
(b)
0
2
E 2 d ,
all space
1
Vd .
2
Pr

PHYS 3033 Assignment 5
Due: 18 Oct 2013 at begin of lecture at 4:30 pm
Problem 1.
Consider a spherical shell of Radius R. There is vacuum, with no charges, both inside and
outside the shell. A surface charge density ( ) = 0 (3cos2 -1) is glued to the surf

Phys-3033 Midterm examination
30 October 2013, 4:30 5:50
Solve all 4 problems! (in total 40 points)
Problem 1: Dipole above infinite grounded plane [10 points]
A dipole of dipole moment p is formed by two charges +q and q, separated by a distance a. p is

Phys-3033 Midterm examination
30 October 2012, 12:00 13:20
Solve all problems (in total 50 points)
Problem 1: Electrostatic field and potential [10 points]
One of these is an impossible electrostatic field. Which one?
(a)
(b)
(k is a constant with the app

Name: _
Student ID: _
Session: T _
PHYS 3033 Electricity and Magnetism I
Quiz 2
Time allowed: 15 minutes
18 September 2013
Divergence in spherical coordinates:
v=
1 2
1
1
r v r )+
sin v ) +
v
(
(
2
r sin
r sin
r r
Suppose the electric field in some regi

Name: _
Student ID: _
PHYS 3033 Electricity and Magnetism I
Quiz 4
2 October 2013
Time allowed 20 minutes
Method of Image Charges
When a cloud passes over a certain spot (point 0) on the surface of the earth a vertical electric field of E
= 100 V/m is rec

Name: _
Student ID: _
PHYS 3033 Electricity and Magnetism I
Quiz 3
25 September 2013
Time allowed 20 minutes
a) Find the electric field due to the following volume charge distribution:
Where
and 0 and R are constants.
b) Using the result of a), find the e

Name: _ Student ID: _ Session: T _
PHYS 3033 - Electricity and Magnetism I
Quiz 1
Time allowed: 30 minutes
11 Sep 2013
Area integral:
da dxdy dydz dzdx (Cartesian) r 2 sin d d (Spherical)
Volume integral:
d dxdydz (Cartesian) r 2 sin drd d (Spherical)
1.

Name: _ Student ID:_ Session: T _
PHYS 3033 - Electricity and Magnetism I
Quiz 8
Time allowed: 20 minutes
13 Nov 2013
1. Check that
A r
0
4
J r
r
is consistent with
d
B r
0
4
J r r
r
2
.
d
Please prove that across a point on a surface at which the

Name: _ Student ID: _ Session: T _
PHYS 3033 - Electricity and Magnetism I
Quiz 7: 23 Oct 2013
Time allowed: 20 minutes
A (free) point charge q is embedded at the center of a linear dielectric sphere with
radius R and permittivity .
(a) Obtain, in terms o

Name: _ Student ID: _ Session: T _
PHYS 3033 - Electricity and Magnetism I
Quiz 6: 16 Oct 2013
Time allowed: 15 minutes
(a) Show that the dipole moment of a pair of charges, +q and q, separated by a
distance d, is coordinate-independent and given by p = q

Name: _ Student ID5_ Session: T _
PHYS 3033 - Electricity and Magnetism I
Quiz 9
Time allowed: 15 minutes
20 Nov 2013
Just above and below the interface between two linear magnetic media the directions
of the magnetic fields change, as shown in the figure