Patel, Kinal – Homework 3 – Due: Jan 29 2008, 7:00 pm – Inst: Weathers
1
This
printout
should
have
13
questions.
Multiplechoice questions may continue on
the next column or page – find all choices
before answering.
The due time is Central
time.
001
(part 1 of 4) 10 points
A uniformly charged ring of radius 9
.
1 cm has
a total charge of 88
μ
C.
The
value
of
the
Coulomb
constant
is
8
.
98755
×
10
9
N
·
m
2
/
C
2
.
Find the magnitude of the electric field on
the axis of the ring at 0
.
72 cm from the center
of the ring.
Correct answer: 7
.
4863
×
10
6
N
/
C.
Explanation:
Let :
a
= 9
.
1 cm = 0
.
091 m
,
Q
= 88
μ
C = 8
.
8
×
10

5
C
,
k
e
= 8
.
98755
×
10
9
N
·
m
2
/
C
2
,
and
x
= 0
.
72 cm = 0
.
0072 m
.
The electric field is
E
=
k
e
x Q
(
x
2
+
a
2
)
3
/
2
=
(8
.
98755
×
10
9
N
·
m
2
/
C
2
) (0
.
0072 m)
(0
.
0072 m
2
+ 0
.
091 m
2
)
3
/
2
×
(8
.
8
×
10

5
C)
=
7
.
4863
×
10
6
N
/
C
.
002
(part 2 of 4) 0 points
Find the magnitude of the electric field on the
axis of the ring at 6
.
89 cm from the center of
the ring.
Correct answer: 3
.
66451
×
10
7
N
/
C.
Explanation:
Let :
x
= 6
.
89 cm = 0
.
0689 m
.
E
=
(8
.
98755
×
10
9
N
·
m
2
/
C
2
) (0
.
0689 m)
(0
.
0689 m
2
+ 0
.
091 m
2
)
3
/
2
×
(8
.
8
×
10

5
C)
=
3
.
66451
×
10
7
N
/
C
.
003
(part 3 of 4) 0 points
Find the magnitude of the electric field on the
axis of the ring at 16 cm from the center of
the ring.
Correct answer: 2
.
02913
×
10
7
N
/
C.
Explanation:
Given :
x
= 16 cm = 0
.
16 m
.
E
=
(8
.
98755
×
10
9
N
·
m
2
/
C
2
) (0
.
16 m)
(0
.
16 m
2
+ 0
.
091 m
2
)
3
/
2
×
(8
.
8
×
10

5
C)
=
2
.
02913
×
10
7
N
/
C
.
004
(part 4 of 4) 10 points
Find the magnitude of the electric field on the
axis of the ring at 136
.
985 cm from the center
of the ring.
Correct answer: 418706 N
/
C.
Explanation:
Let :
x
= 136
.
985 cm
.
E
=
(8
.
98755
×
10
9
N
·
m
2
/
C
2
) (1
.
36985 m)
(1
.
36985 m
2
+ 0
.
091 m
2
)
3
/
2
×
(8
.
8
×
10

5
C)
=
418706 N
/
C
.
Comment:
The interesting thing to note
here is that the field first increases from (a)
to (b), then decreases from (b) to (c) and
also from (c) to (d).
Thus, we should have
a maximum somewhere between
x
= 0
.
72 cm
and
x
= 16 cm. In fact, the maximum is at
x
max
=
a
√
2
= 6
.
43467 cm
.
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 Spring '08
 Weathers
 Electron, Work, Correct Answer, Electric charge, patel

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