Question

The electric potential $V$ at any point $P(x,y,z)$ in space is given by$V=4x^{2}V$. The electric field at the point $(1m,2m)$ is:

• A. $-8\hat{i}$
• B. $8\hat{i}$
• C. $-16\hat{i}$
• D. $16\hat{i}$

Answer 1

The correct option is A $-8\hat{i}$

$V=4x^{2}V$

$\overrightarrow{E}=-\frac{\partial V}{\partial x}\hat{i}-\frac{\partial V}{\partial y}\hat{j}-\frac{\partial V}{\partial z}\hat{k}$

Here, $\frac{\partial V}{\partial x}=8x$

and, $\frac{\partial V}{\partial y}=\frac{\partial V}{\partial z}=0$

Hence, $\overrightarrow{E}=-8x\hat{i}$

Given point is $(1,2)$ that is $x=1,y=2$

Hence, $\overrightarrow{E}=-8\hat{i}N/C$

Answer-(A)