PHYS 241
Ch. 28 Homework Solutions
28.3.
I
DENTIFY
:
A moving charge creates a magnetic field.
S
ET
U
P
:
The magnetic field due to a moving charge is
0
2
sin
4
qv
B
r
μ
φ
π
=
.
E
XECUTE
:
Substituting numbers into the above equation gives
(a)
7
19
7
0
2
6
2
sin
4
10
T
m/A (1.6
10
C)(3.0
10
m/s)sin30
.
4
4
(2.00
10
m)
qv
B
r
μ
φ
π
π
π



×
⋅
×
×
°
=
=
×
B
= 6.00
×
10
–8
T, out of the paper, and it is the same at point
B
.
(b)
B
= (1.00
×
10
–7
T
⋅
m/A)(1.60
×
10
–19
C)(3.00
×
10
7
m/s)/(2.00
×
10
–6
m)
2
B
= 1.20
×
10
–7
T, out of the page.
(c)
B
= 0 T since sin(180°) = 0.
E
VALUATE
:
Even at high speeds, these charges produce magnetic fields much less than the Earth’s
magnetic field.
28.9.I
DENTIFY
:
A current segment creates a magnetic field.
S
ET
U
P
:
The law of Biot and Savart gives
0
2
sin
4
Idl
dB
r
μ
φ
π
=
.
E
XECUTE
:
Applying the law of Biot and Savart gives
(a)
7
2
4π
10
T
m/A (10.0 A)(0.00110 m) sin90°
4π
(0.0500 m)
dB

×
⋅
=
= 4.40
×
10
–7
T, out of the paper.
(b)
The same as above, except
2
2
(5.00 cm)
(14.0 cm)
r
=
+
and
φ
= arctan(5/14) = 19.65°, giving
dB
=
1.67
×
10
–8
T, out of the page.
(c)
dB
= 0 since
φ
= 0°.
E
VALUATE
:
This is a very small field, but it comes from a very small segment of current.
28.13.
I
DENTIFY
:
A current segment creates a magnetic field.
S
ET
U
P
:
The law of Biot and Savart gives
0
2
sin
.
4
Idl
dB
r
μ
φ
π
=
Both fields are into the page, so their
magnitudes add.
E
XECUTE
:
Applying the Biot and Savart law, where
2
2
1
2
(3.00 cm)
(3.00 cm)
r
=
+
= 2.121 cm, we
have
7
2
4π
10
T
m/A (28.0 A)(0.00200 m)sin 45.0°
2
4π
(0.02121 m)
dB

×
⋅
=
= 1.76
×
10
–5
T, into the paper.
E
VALUATE
:
Even though the two wire segments are at right angles, the magnetic fields they create are
in the same direction.
28.15.
I
DENTIFY
:
We can model the lightning bolt and the household current as very long currentcarrying
wires.
S
ET
U
P
:
The magnetic field produced by a long wire is
0
2
I
B
r
μ
π
=
.
E
XECUTE
:
Substituting the numerical values gives
(a)
B =
7
(4π
10
T
m/A)(20,000 A)
2π(5.0 m)

×
⋅
= 8
×
10
–4
T
(b)
7
(4π
10
T
m/A)(10 A)
2π(0.050 m)
B

×
⋅
=
= 4.0
×
10
–5
T.
E
VALUATE
:
The field from the lightning bolt is about 20 times as strong as the field from the
household current.
28.21.
I
DENTIFY
:
0
2
I
B
r
μ
π
=
. The direction of
B
r
is given by the righthand rule in Section 20.7.
1
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
S
ET
U
P
:
Call the wires
a
and
b
, as indicated in Figure 28.21. The magnetic fields of each wire at
points
P
1
and
P
2
are shown in Figure 28.21a. The fields at point 3 are shown in Figure 28.21b.
This is the end of the preview.
Sign up
to
access the rest of the document.
 Fall '08
 Milsom
 Charge, Magnetism, Work, Magnetic Field

Click to edit the document details