Question

Find the potential difference between $(0,-2,3)$ and $(1,3,4)$ for the electric field $\overrightarrow{E}=5\hat{i}-\hat{k}$ in space.

• A. $-4\text{V}$
• B. $-6\text{V}$
• C. $12\text{V}$
• D. $-8\text{V}$

Answer 1

The correct option is A $-4\text{V}$

Given:
$\overrightarrow{E}=5\hat{i}-\hat{k}$
Points $(0,-2,3)$ and $(1,3,4)$

We know that,
$\Delta V=-\overrightarrow{E}.\left[\Delta r\right]$
So,
$\Delta r=(\hat{i}+3\hat{j}+4\hat{k})-(-2\hat{j}+3\hat{k})$

$\Delta r=(\hat{i}+5\hat{j}+\hat{k})$

Now, $\Delta V=-(5\hat{i}-\hat{k}).(\hat{i}+5\hat{j}+\hat{k})$

$\Delta V=-(5-0-1)=-4\text{V}$

Hence, option $\left(A\right)$ is correct.