Chapter 21: Coulomb’s Law
PHY2049: Chapter 21
1
1. What is net force on central –q charge?
−q
PHY2049: Chapter 21
2
Answer to Question #1
ÎThe
central charge is surrounded on all sides by charges
that are equal and on opposite sides, so the forces cancel
each other.
ÎThe
only exception is the +2q charge above the central
charge. Thus the net force on the central charge is
upward (attraction) with magnitude
F=
2kq 2
r2
PHY2049: Chapter 21
3
2. Rank by magnitude of force.
Assume charges are equally spaced.
PHY2049: Chapter 21
4
Answer to Question #2
Î#3
has largest magnitude because all charges cause a
force in the same direction.
Î#4
has zero magnitude (smallest), because charges of
equal magnitude are located equal distances on opposite
sides.
Î#1
is second largest because outer charges cancel and
inner charges add.
Î#2
is third largest because inner charges cancel and outer
charges add.
ÎSo
the ranking (smallest to largest) 4, 2, 1, 3
PHY2049: Chapter 21
5
3. What is magnitude and direction of
force on charge q > 0? Assume charges
are on perfect square of side L.
−Q
+Q
x
q
−Q
+Q
PHY2049: Chapter 21
6
Answer to Question #3
ÎForces
cancel in y direction, so only x component remains
(it is the same for all 4 charges)
Fx = 4 ×
kQq
(
L/ 2
)
2
cos 45° =
2
L
−Q
+Q
G
F
x
q
+Q
4 2kQq
−Q
PHY2049: Chapter 21
7
4. Where should one put a 3rd charge
so that it feels no net force?
PHY2049: Chapter 21
8
Answer to Question #4
ÎLet’s
just do (a). The others are very similar.
ÎThe
third charge must be on the left side. At some
distance, the force from the +q charge (closer) will cancel
the force from the -3q charge (farther).
ÎLet
the distance between the first two charges be called L
and +q be at x = 0. The position of the third charge is
defined as x, where x < 0. The forces on the third charge
can be written
Fx = −
kqq3
x
2
+
3kqq3
( L − x)
L
x=−
=−
3 −1
(
=0
2
) L −1.37 L
3 +1
2
PHY2049: Chapter 21
9
What is the location and magnitude of 3rd
charge where all three are in equilibrium?
PHY2049: Chapter 21
10
Answer to Question #5
ÎWe
see immediately that the 3rd charge must lie between
the charges, but closer to –q than to –3q (why?).
ÎLet
the two charges be at x = 0 & L and let the 3rd charge
be at location x. Then Fx = 0 on the 3rd charge yields
Fx = −
3kqq3
x
2
+
kqq3
( L − x)
2
=0
3L 3 − 3
x=
=
L 0.634 L
2
3 +1
ÎNote
that q3 must be opposite sign as q to make the other
charges be in equilibrium. To find q3, require Fx = 0 on the
1st charge from the other two charges
Fx =
3kqq3
x
2
−
3kq
2
L
2
2
=0
6−3 3
⎛x⎞
q3 = ⎜ ⎟ q =
q 0.40q
2
⎝L⎠
PHY2049: Chapter 21
11