Question

The electric potential varies in space according to the relation $V=3x+4y.$ A particle of mass $0.1kg$ starts from rest from point $(2,3.2)$ under the influence of this field. The charge on the particle is $+1\mu C.$ Assume V and $(x,y)$ are in S.I. units
The component of electric field in the y - direction $\left(E_y\right)$ is

• A. $3V{m}^{-1}$
• B. $-4V{m}^{-1}$
• C. $5V{m}^{-1}$
• D. $8V{m}^{-1}$

Answer 1

The correct option is B $-4V{m}^{-1}$

$V=3x+4y$
We know that the relation between $V$ and $E$ is given by
$E=-[\frac{\delta V}{\delta x}\hat{i}+\frac{\delta V}{\delta y}\hat{j}+\frac{\delta V}{\delta z}\hat{k}]$
$⟹E_x=-\frac{\delta V}{\delta x}\hat{i}$
$\therefore E_x=-3V{m}^{-1}$
Similarly, $E_y=-\frac{\delta V}{\delta y}\hat{j}$
$\therefore E_y=-4V{m}^{-1}$