Fundamentals of Physics Extended (10th Edition)

Published by Wiley
ISBN 10: 1-11823-072-8
ISBN 13: 978-1-11823-072-5

Chapter 24 - Electric Potential - Questions - Page 709: 5c

Answer

The work done by the electric force due to Sphere B is negative.

Work Step by Step

We can write a general equation for the electric potential around a point charge: $V = \frac{1}{4\pi~\epsilon_0}~\frac{q}{r}$ Sphere B is positively charged so $V \gt 0$ at all points. As $r$ decreases, the magnitude of $V$ increases. Therefore, sphere A would be moved to a higher electric potential. That is $~~V_f \gt V_i$ We can find an expression for the work done by the electric force due to Sphere B: $Work = -\Delta U = -(q_A~\Delta V) = -q_A~(V_f-V_i)$ $q_A \gt 0~~$ and $~~(V_f - V_i) \gt 0$ Therefore, the work done by the electric force due to Sphere B is negative.
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