1. Coulomb’s Law Problems
1. Find the force between charges of +1.0 C
and -2.0 C located 0.50 m apart in air.
k q1 q2
F = r2
( 9 x 109 Nm2/C2 )( +1.0 C )( -2.0 C ) =
( 0.50 m)2
F = x 1010 N
negative sign indicates attraction

2. 2. q1 = μC F = N r = m
(a) What is the sign of the second charge?
A positive force indicates repulsion, and since
q1 is negative, q2 must also be negative

3. 2. q1 = μC F = N r = m
(b) What is the magnitude of the second charge? q2 = ?
k q1 q2
Solve for q2 r2
F = r2 r2
r2 F = k q1 q2
k q1
k q1
r2 F
( 0.30 m )2 ( N )
q2 = =
k q1
( 9 x 109 Nm2/C2 )( x 10-6 C )
q2 = C
= x 10-6 C
= μC
must change μC to C

4. 3. F = N q1 = q2 = x 10-6 C r = ?
k q1 q2
Solve for r r2
F = r2 r2
r2 F = k q1 q2
k q1 q2
r2 = F F F
k q1 q2
r = F
(9 x 109 Nm2/C2)(5 x 10-6 C)(5 x 10-6 C) =
0.25 N
r = m (don’t forget to take square root)

5. 4. Two spheres, with charges +20.0 μC and -10.0 μC,
are 10.0 cm apart. Find force of attraction.
q1 = x 10-6 C q2 = x 10-6 C
k q1 q2
F = r2
(9 x 109 Nm2/C2)(+20.0 x 10-6C)(-10.0 x 10-6 C) =
( 0.10 m)2
F = N

6. 5. The spheres are touched and separated again. What is the force?
When the spheres are touched,
the charge re-distributes
+10 μC
-10μC
If each sphere had the same charge, but of opposite sign, the net charge would be zero (the sum of +10 and -10 is zero)
+10 μC
-10μC
Both spheres neutral N N

7. 5. The spheres are touched and separated again. What is the force?
With one sphere +20 μC and the
other -10 μC, the
overall charge is
(+20) + (-10) = +10 μC
+20 μC
-10μC
+20 μC
-10μC
When the spheres are touched, the +10 μC distributes so that each sphere has +5 μC
+5.0 μC
+5.0 μC
+5.0 μC
+5.0 μC

8. Two spheres, each with charge +5.0 μC, are 10.0 cm
apart. Find force of attraction.
q1 = +5.0 x 10-6 C q2 = +5.0 x 10-6 C
k q1 q2
F = r2
(9 x 109 Nm2/C2)(+5.0 x 10-6C)2 =
( 0.10 m)2
F = N

9. 6. Find the distance between two spheres, one -3.0 x 10-5 C
and the other -2.5 x 10-4 C, if the electric force is 1.0 N.
k q1 q2
Solve for r r2
F = r2 r2
r2 F = k q1 q2
k q1 q2
r2 = F F F
k q1 q2
r = F
(9 x 109 Nm2/C2)(-3 x 10-5 C)(-2.5 x 10-4 C) =
1.0 N
r = m (don’t forget to take square root)

10. 7. A sphere of charge +3.5 μC experiences a force of
-3.0 N when separated by a second sphere by 0.25 m.
Find the charge of the second sphere.
k q1 q2
Solve for q2 r2
F = r2 r2
r2 F = k q1 q2
k q1
k q1
r2 F
( 0.25 m )2 ( N )
q2 = =
k q1
( 9 x 109 Nm2/C2 )( x 10-6 C )
q2 = C
= x 10-6 C
= μC
must change μC to C