Chapter 17, Problem 11Q

To determine

What can you infer about the electric potential V if the electric field $\overrightarrow{E}$ is uniform in a region? If V is uniform in a region of space, what can you infer about $\overrightarrow{E}$

?

Answer to Problem 11Q

Solution:

When V is uniform electric field is zero.

Explanation of Solution

We have the relation between electric field, $\overrightarrow{E}$ and potential difference V with change in distance given by $\overrightarrow{E}=\frac{\Delta V}{\Delta x}$

When $\overrightarrow{E}$ is uniform we have $\overrightarrow{E}=\frac{\Delta V}{\Delta x}$ = Constant, Assume $\overrightarrow{E}=5\frac{\text{V}}{\text{m}}$, which implies there is a 5V potential increase with 1 m.

When V is uniform we have $\overrightarrow{E}=\frac{\Delta V}{\Delta x}$ = Zero, which implies when V is uniform electric field is zero.