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Chapter 22: Electric Fields
Problem 1
In Fig. 2230 the electric field lines on the
left have twice the separation as those on the
right. (a) If the magnitude of the field at A is
40 N/C, what force acts on a proton at A?
(b) What is the magnitude of the field at B?
Answer
(a) 6.40
×
10
18
N. (b)
≈
20 N/C.
B
A
Figure 2230
Solution
(a)
If E is the magnitude of the electric field at A then the magnitude of the force on the
proton is
F
=
qE,
(q is the magnitude of the charge on proton)
F
=
(1.60
×
10
19
C)*(40 N/C)
F
=
6.40
×
10
N
(b)
Note that the field lines at B are about twice as far apart as at A. Since the density of
the field lines represents the magnitude of the electric field this means that the magnitude of
the field at B is about half of that at A or
≈
20 N/C.
Problem 3
What is the magnitude of a point charge whose electric field 50 cm away has the magnitude
of 2.0 N/C?
Answer
56 pC
The magnitude of the electric field due to a point charge q at a point at a distance r from the
point charge is
E
=
1
4
πε
o
q
r
2
Therefore the magnitude of the charge is
q
=
4
πε
o
r
2
E
=
0.50
m
( )
2
2.0
N/C
( )
8.99
×
10
9
N
⋅
m
2
C
2
=
56
pC
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Chapter 22: Electric Fields
Problem 8
(a) In Fig. 2231, two point charges q
1
= 5q and q
2
= +2q are fixed to the x axis. (a) As a
multiple of distance L, at what coordinate on the axis is the net electric field of the particles
zero? (b) Sketch the electric field lines.
L
x
y
q
1
q
2
Figure 2231
Answer
(a) 1.72L to the right of q
2
.
Solution
(a)
We can set up the equations for this problem if we will first determine possible
regions in which the electric field could be zero. Referring to Diagram 8a, note first of all
that the field cannot be zero accept along the line that runs through the two point charges.
Furthermore by looking at the directions and relative sizes of the electric fields due to the
two charges individually in three intervals along this line we see that any points where the
field is zero must lie to the right of q
2
.
L
x
y
q
1
q
2
E
q
1
q
2
E
q
2
E
q
2
E
E
q
1
E
q
1
Diagram 8a
Therefore if the field is zero it is at a point (x,0) where x > L.
The total electric field at such
a point is
E
tot
=
1
4
πε
o
q
1
r
1
3
r
1
+
1
4
πε
o
q
2
r
2
3
r
2
where
r
1
is the vector from q
1
to the point (x,0) and
r
2
is the vector from q
2
to the point
(x,0).
Which means that
r
1
= x
i
and
r
2
= (x  L)
i
. Therefore if the total electric field is zero
the previous equation for
E
tot
becomes
0
=
1
4
πε
o
−
5
q
x
3
x
i
+
1
4
o
2
q
x
−
L
( )
3
x
−
L
( )
i
or
0
=
−
5
x
2
+
2
x
−
L
( )
2
or
3x
2
– 10Lx + 5L
2
= 0.
Chapter 22: Electric Fields
223
Solving this quadratic equation for x yields x = 0.61L or x = 2.72L.
According to our
previous analysis x must be greater than L therefore we find that the field will be zero at a
point 1.72L to the right of the q
2
.
(b)
A sketch of the field lines is shown in Diagram 8b. Notice in the sketch how the
field is more strongly affected by the 5q charge. For quite a distance from the 5q charge
the field still looks like that due to a single point charge as if the +2q charge were not
present. In the vicinity of the +2q charge however the field deviates from the radial field
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 Spring '09
 C
 Physics, Electric Fields, Force

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