The Hong Kong University of Science and Technology
Honors Electricity and Magnetism I
PHYS 3053

Fall 2015
Course Webpage:
http:/teaching.phys.ust.hk/Phys3033/
http:/teaching.phys.ust.hk/Phys3053/
Vector Analysis
What is a vector?
A vector in n dimension is any set
of ncomponents that transforms in
the same manner as a displacement
when you change coordinates
The Hong Kong University of Science and Technology
Honors Electricity and Magnetism I
PHYS 3053

Fall 2015
1. To show that
q
2
S R 2 + z 2 2Rz cos 3/ 2 sin d d = 4 0 z
(
)
0
R2
Ez =
4 0
z R cos
for z > R
for z < R
Solution:
Ez =
R2
4 0
2
0
d
0
( z R cos ) sin d
(R
2
+ z 2 2 Rz cos )
=
0 ( z R cos ) d ( cos )
R2
2
3/ 2
4 0
( R 2 + z 2 2Rz cos )
=
R2
2
The Hong Kong University of Science and Technology
Honors Electricity and Magnetism I
PHYS 3053

Fall 2015
PHYS 3033/3053 Assignment 1
Due: 11 Sep 2015 at begin of lecture at 3:00 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
The Hong Kong University of Science and Technology
Honors Electricity and Magnetism I
PHYS 3053

Fall 2015
Electrostatics
What is the force exerted on a
test charge Q, by some source
charges q1 , q2 , q3 , ?
Q
q
6
q2
q5
q1
q4
q3
qi
.
source charges
F = ?
test charge
Principle of superposition:
. The interaction between any two charges is completely
unaffecte
The Hong Kong University of Science and Technology
Honors Electricity and Magnetism I
PHYS 3053

Fall 2015
PHYS 3033/3053
Assignment 3 Solution
Problem 1.
Consider a spherical shell with radius R and surface charge density:
The electric field is given by:
(a) Find the energy stored in the field by:
(b) Find the energy stored in the field by:
And compare the re
The Hong Kong University of Science and Technology
Honors Electricity and Magnetism I
PHYS 3053

Fall 2015
PHYS 3033/3053
Assignment 2 Solution
Problem 1.
(a) Find the electric field vector (magnitude and direction) at a distance z above the midpoint between two equal
positive charges, +q, which are separated by a distance d (see figure below for a sketch). Ch
The Hong Kong University of Science and Technology
Honors Electricity and Magnetism I
PHYS 3053

Fall 2015
PHYS 3033/3053
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
The Hong Kong University of Science and Technology
Honors Electricity and Magnetism I
PHYS 3053

Fall 2015
PHYS 3033/3053 Assignment 1
Due: 14 Sep 2016 at begin of tutorial at 6:00 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