ECE 329
Homework 2
Due: Jan 28, 2008, 5PM
1. In this problem we will compare the magnitudes of electrical force
q
E
and magnetic force
q
v
×
B
on
a moving test charge
q
due to fields
E
and
B
produced by another charge
Q
at some distance
r
.
a) Let
E
be the static Coulomb field of
Q
with magnitude
Q
4
πǫ
o
r
2
. Also let
B
the magnetic field
calculated using BiotSavart law with a maximum magnitude
μ
o
I

d
l

4
πr
2
where for
I

d
l

we can use
QV
s
, where
V
s
denotes the speed of charge
Q
when it is moving to produce
B
. Denoting the
speed of the test charge as
v
q
, show that the magnetic force on
q
can be as strong as the electric
force only in the limit when the product of
v
q
and
V
s
approaches
c
2
≡
1
μ
o
ǫ
o
, where
c
≈
3
×
10
8
m/s. Hint: what is the expression for the largest possible magnitude for the ratio of
q
v
q
×
B
and
q
E
?
b) The result of part (a) shows that magnetic force is typically much weaker than the electro
static force (when elementary sources are considered one at a time).
Why then are magnetic
effects observed in everyday life (e.g., pull and push of refrigerator magnets) often stronger than
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 Spring '08
 FRANKE
 Electromotive Force, Magnetic Force, Magnetic Field, Electric charge, right hand rule

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