The
emf
induced in the circuit is
10.0points
A concave mirror has a radius of curvature of
0
.
726 m. An object is placed 2
.
41 m in front
of the mirror.
What is the position of the image?
011
10.0points
In a thundercloud there may be an electric
charge of 43 C near the top and
−
43 C near
the bottom. These charges are separated by
approximately 2
.
2 km.
What is the magnitude of the electric force
between them?
The Coulomb constant is
Since the charges are of opposite signs, this
force is attractive.
012
10.0points
A concave mirror has a radius of curvature of
0
.
726 m. An object is placed 2
.
41 m in front
of the mirror.
What is the position of the image?

8
.
98755
×
10
9
N
·
m
2
/
C
2
.
013
10.0points

Version 036 – Final 58010 Fall 14 – yeazell – (58010)
7
Two parallel wires carry equal currents in
the opposite directions.
Point
A
is midway
between the wires, and
B
is an equal distance
on the other side of the wires.
A
B
What is the ratio of the magnitude of the
magnetic field at point A to that at point
B
?
1.
B
A
B
B
= 3
correct
2.
B
A
B
B
=
1
2
3.
B
A
B
B
=
1
3
4.
B
A
B
B
= 0
5.
B
A
B
B
=
2
3
6.
B
A
B
B
=
5
2
7.
B
A
B
B
= 4
8.
B
A
B
B
=
10
3
9.
B
A
B
B
=
4
3
10.
B
A
B
B
= 2
Explanation:
The magnetic field due to a long wire is
B
=
μ
0
I
2
π r
.
Let the distance between the wires be
r
.
The magnetic field at A due to the upgoing
wire is
B
up,A
=
μ
0
I
2
π
(
r/
2)
=
μ
0
I
π r
.
The right-hand rule tells us the direction is
into the paper.
Due to the fact that A is
the same distance from both wires, the other
wire gives a magnetic field at A of the same
magnitude, also directed into the paper due
to the right-hand rule.
The total magnetic
field at A is
B
A
= 2
B
up,A
=
2
μ
0
I
π r
.
Now, the field at B due to the upgoing wire is
B
up,B
=
μ
0
I
2
π
(3
r/
2)
=
μ
0
I
3
π r
,
again into the paper, while
B
down,B
=
μ
0
I
2
π
(
r/
2)
=
μ
0
I
π r
out of the paper. So
B
B
=
B
down,B
−
B
up,B
=
μ
0
I
π r
parenleftbigg
1
−
1
3
parenrightbigg
=
2
μ
0
I
3
π r
,
out of the paper. Comparing magnitudes, we
find
B
A
B
B
=
2
μ
0
I
π r
2
μ
0
I
3
π r
= 3
.
014
10.0points
An electron is projected into a uniform mag-
netic field given by
vector
B
=
B
x
ˆ
ı
+
B
y
ˆ
.
The magnitude of the charge on an electron
is
e
.
x
y
z
v
electron
B
x
B
y
B

Version 036 – Final 58010 Fall 14 – yeazell – (58010)
8
Find the magnetic force when the velocity
of the electron is
v
ˆ
.
6.
eB
y
v
ˆ
i