## Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (4th Edition)

Published by Pearson

# Chapter 22 - Electric Charges and Forces - Conceptual Questions: 14

#### 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.

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