#### Answer

(a) The magnitude of the force on A is 4F
(b) The magnitude of the force on B is 4F

#### Work Step by Step

We can use Coulomb's law to find the magnitude $F$:
$F = \vert \frac{1}{4\pi~\epsilon_0}~\frac{q_A~q_B}{d^2}\vert$
$F$ is the magnitude of the force on A, and $F$ is the magnitude of the force on B.
(a) We can write an expression for the magnitude of the new force after the charge of B is increased by a factor of 4.
$F' = \vert\frac{1}{4\pi~\epsilon_0}~\frac{q_A~(4q_B)}{d^2}\vert$
$F' = 4~\vert \frac{1}{4\pi~\epsilon_0}~\frac{q_A~q_B}{d^2}\vert$
$F' = 4F$
The magnitude of the force on A is 4F.
(b) Similar to part (a), the magnitude of the force on B is 4F.