Physics Chapter 16 Solutions Electrostatics Worksheet II
Solutions Electrostatics Worksheet II
1.
!" F 4.0x10 !17 N
E= =
= 250 N/C q 1.6x10 !19 C
2.
!"
F = Eq = 75N/C * 2 *1.6x10 !19 C = 2.4x10 !19 N
3.
!" F
0.24N
3
E= =
=
1.2x10
N/C
!4 q 2x10 C
a.
N • m2
* 5x10 !9 C
!" ke q 9x10
2
C
E= 2 =
= 500 N/C r (0.3m)2
b.
N • m2
!9
!10
9x10
*
5x10
C
*
4x10
C
2 ke q1 q2
C
F=
=
= 2x10 !7 N
2
2 r (0.3m)
a.
!" F 2.0x10 !3 N
E= =
= 330 N/C q 6x10 !6 C
b.
!"
F = Eq = 330N/C * 2.0x10 !6 C = 6.7x10 !4 N
9
4.
9
5.
N • m2
9x10
* 3C
!"
2 ke q
C
E = 2* 2 = 2*
= 2.16x1011 N/C
2
r
(0.5m)
2
6.
7.
a.
!
!E =
ke q1 ke q2
+ 2 = r2 r
N • m2
C 2 ( q + q ) = 9x10 5 N/C
1
2
(0.5m)2
9x10 9
b.
ke q1
ke q2
= 2
2
r
(r +.1)
(r +.1) r2 2
q
= 1 q2 r +.1 = 2r
8.
9.
r +.1 q1 2x10 !7 C
=
=
=2
!8 r q2
5x10 C r = 0.1m to the right of q 2 . why?
!"
F = mg = Eq = 2x014 N/C*3.2x10 !19 C = 6.4x10 !19 N
Feʼ
T
!
mgʼ
Fr
Fe mg " = 30˚ Fe' = mgsin(" ) mg' = mgcos(" )
Fe'
tan(" ) = so that Fe = mgtan(" )but mg' Ke * Q2
Fe =
= mgtan(" ) so that Q =
2
r
mgtan(" )r2
Ke
1x10 #4 kg * 9.8m /s2 * 0.577 * .4m2 substitute in Q =
= 1.0x10 #7 C = .1µC
2
N•m
9.0x109
C2
!
"Pe 5.0x10 #18 J
= 31.3V
10. V = q =
#19
1.6x10
C
11.
a.
N•m
2.0x10 "16 C * 2.0x10 "10 C * 9.0x109 qQKe C2
Pe =
=
R
.01m
N•m
2.0x10 "10 C * 9.0x109
QKe
C2
V
=
=
b.
R
.01m
!
2
= 3.6x10 "14 J
2
= 180V
$1
1 '
"Pe = Ke * Q1*Q2 * & #
)=
% R1 R2 (
!
12. a.
!
b.
N • m2
#19
9
3C *1.6x10
C * 9.0x10
= 3.24 x10 #9 J
2
C
W 3.24 x10 "9 J
W = Fd therefore F =
=
= 1.08x10 "8 N d 0.3m
13.
!
a.
!
Ea =
Ke q
R2
Eb =
Ke q
R2
N • m2
9
9.0x10
* 6x10 "6 C
C2
=
= 2.16x105 N /C
(0.5m)2
N • m2
9
9.0x10
* 8x10 "6 C
2
C
=
= 1.28x105 N /C
2
(0.5m)
Mag = E a2 + E b2 = 2.51x105 N /C
!
!
!
#
5 N /C &
2.16x10
"1
( =59˚
E =Tan %%
(
5
$ 1.28x10 N /C '
b.
N • m2
9
9.0x10
* 9.0x10 "6 C
Ke * q
C2
Va =
=
= 1.08x105 V r 0.5m
N • m2
9
9.0x10
* "8x10 "6 C
2
Ke * q
C
Vb =
=
= "0.96x105 V r 0.5m
Total
1.2x10 4 V
!
14.
E=
F q Fa = 2.16x105 N /c * 9x10 "6 C = 1.944N
Fb = 1.28x105 N /c
1.
!" F 4.0x10 !17 N
E= =
= 250 N/C q 1.6x10 !19 C
2.
!"
F = Eq = 75N/C * 2 *1.6x10 !19 C = 2.4x10 !19 N
3.
!" F
0.24N
3
E= =
=
1.2x10
N/C
!4 q 2x10 C
a.
N • m2
* 5x10 !9 C
!" ke q 9x10
2
C
E= 2 =
= 500 N/C r (0.3m)2
b.
N • m2
!9
!10
9x10
*
5x10
C
*
4x10
C
2 ke q1 q2
C
F=
=
= 2x10 !7 N
2
2 r (0.3m)
a.
!" F 2.0x10 !3 N
E= =
= 330 N/C q 6x10 !6 C
b.
!"
F = Eq = 330N/C * 2.0x10 !6 C = 6.7x10 !4 N
9
4.
9
5.
N • m2
9x10
* 3C
!"
2 ke q
C
E = 2* 2 = 2*
= 2.16x1011 N/C
2
r
(0.5m)
2
6.
7.
a.
!
!E =
ke q1 ke q2
+ 2 = r2 r
N • m2
C 2 ( q + q ) = 9x10 5 N/C
1
2
(0.5m)2
9x10 9
b.
ke q1
ke q2
= 2
2
r
(r +.1)
(r +.1) r2 2
q
= 1 q2 r +.1 = 2r
8.
9.
r +.1 q1 2x10 !7 C
=
=
=2
!8 r q2
5x10 C r = 0.1m to the right of q 2 . why?
!"
F = mg = Eq = 2x014 N/C*3.2x10 !19 C = 6.4x10 !19 N
Feʼ
T
!
mgʼ
Fr
Fe mg " = 30˚ Fe' = mgsin(" ) mg' = mgcos(" )
Fe'
tan(" ) = so that Fe = mgtan(" )but mg' Ke * Q2
Fe =
= mgtan(" ) so that Q =
2
r
mgtan(" )r2
Ke
1x10 #4 kg * 9.8m /s2 * 0.577 * .4m2 substitute in Q =
= 1.0x10 #7 C = .1µC
2
N•m
9.0x109
C2
!
"Pe 5.0x10 #18 J
= 31.3V
10. V = q =
#19
1.6x10
C
11.
a.
N•m
2.0x10 "16 C * 2.0x10 "10 C * 9.0x109 qQKe C2
Pe =
=
R
.01m
N•m
2.0x10 "10 C * 9.0x109
QKe
C2
V
=
=
b.
R
.01m
!
2
= 3.6x10 "14 J
2
= 180V
$1
1 '
"Pe = Ke * Q1*Q2 * & #
)=
% R1 R2 (
!
12. a.
!
b.
N • m2
#19
9
3C *1.6x10
C * 9.0x10
= 3.24 x10 #9 J
2
C
W 3.24 x10 "9 J
W = Fd therefore F =
=
= 1.08x10 "8 N d 0.3m
13.
!
a.
!
Ea =
Ke q
R2
Eb =
Ke q
R2
N • m2
9
9.0x10
* 6x10 "6 C
C2
=
= 2.16x105 N /C
(0.5m)2
N • m2
9
9.0x10
* 8x10 "6 C
2
C
=
= 1.28x105 N /C
2
(0.5m)
Mag = E a2 + E b2 = 2.51x105 N /C
!
!
!
#
5 N /C &
2.16x10
"1
( =59˚
E =Tan %%
(
5
$ 1.28x10 N /C '
b.
N • m2
9
9.0x10
* 9.0x10 "6 C
Ke * q
C2
Va =
=
= 1.08x105 V r 0.5m
N • m2
9
9.0x10
* "8x10 "6 C
2
Ke * q
C
Vb =
=
= "0.96x105 V r 0.5m
Total
1.2x10 4 V
!
14.
E=
F q Fa = 2.16x105 N /c * 9x10 "6 C = 1.944N
Fb = 1.28x105 N /c