Chapter 27
Sources of the Magnetic Field
13
•
[SSM]
At time
t =
0, a particle has a charge of
12
μ
C, is located in the
z
= 0 plane at
x
=
0,
y
=
2.0
m, and has a velocity equal to
i
ˆ
m/s
30
. Find the magnetic field in the
z
= 0 plane at (
a
) the origin, (
b
)
x
=
0,
y
=
1.0 m, (
c
)
x
=
0,
y
=
3.0 m, and (
d
)
x
=
0,
y
=
4.0 m.
Picture the Problem
We can substitute for
v
and
q
in the equation describing the
magnetic field of the moving charged particle (
2
0
ˆ
4
r
q
r
v
B
×
=
π
μ
), evaluate
r
and
r
ˆ
for each of the given points of interest, and then find
B
.
The magnetic field of the moving
charged particle is given by:
2
0
ˆ
4
r
q
r
v
B
×
=
π
μ
Substitute numerical values and
simplify to obtain:
(
29
(
29
(
29
(
29
2
2
2
2
7
ˆ
ˆ
m
pT
0
.
36
ˆ
ˆ
m/s
30
C
12
N/A
10
r
r
r
i
r
i
B
×
⋅
=
×
=

μ
(
a
) Find
r
and
r
ˆ
for the particle at
(0, 2.0 m) and the point of interest at
the origin:
(
29
j
r
ˆ
m
0
.
2

=
,
m
0
.
2
=
r
, and
j
r
ˆ
ˆ

=
Evaluating
(
29
0
,
0
B
yields:
(
29
(
29
(
29
(
29
(
29
k
j
i
B
ˆ
pT
0
.
9
m
0
.
2
ˆ
ˆ
m
pT
0
.
36
0
,
0
2
2

=

×
⋅
=
(
b
) Find
r
and
r
ˆ for the particle at
(0, 2.0 m) and the point of interest at
(0, 1.0 m):
(
29
j
r
ˆ
m
0
.
1

=
,
m
0
.
1
=
r
, and
j
r
ˆ
ˆ

=
Evaluate
(
29
m
0
.
1
,
0
B
to obtain:
(
29
(
29
(
29
(
29
(
29
k
j
i
B
ˆ
pT
36
m
0
.
1
ˆ
ˆ
m
pT
0
.
36
m
0
.
1
,
0
2
2

=

×
⋅
=
(
c
) Find
r
and
r
ˆ for the particle at
(0, 2.0 m) and the point of interest at
(0, 3.0 m):
(
29
j
r
ˆ
m
0
.
1
=
,
m
0
.
1
=
r
, and
j
r
ˆ
ˆ
=