Question

The force experienced by a charged particle of charge $q$ at $(1,1,1)$ is

• A. $-5q\hat{i}$
• B. $5q\hat{i}$
• C. $5q(\hat{i}+\hat{j})$
• D. $-5q(\hat{i}+\hat{j})$

Answer 1

The correct option is A $-5q\hat{i}$

$V=4x^2-3x$

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

$\frac{\partial V}{\partial x}=8x-3$

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

Hence, $\overrightarrow{E}=-(8x-3)\hat{i}$

At, $(1,1,1):-$

$\overrightarrow{E}=-5\hat{i}N/C$

Hence, force $\overrightarrow{F}=q\overrightarrow{E}$

$⟹\overrightarrow{F}=-5q\hat{i}N$

Answer-(A)