The electric potential V at any point (x, y, z) (all in meters) in spaced is given by V = 4x2 volt. The electric field at the point (1m, 0, 2m) in V/m is :

Engineering

Physics

Electric Potential Energy and Electric Potential

Question

The electric potential V at any point (x, y, z) (all in meters) in spaced is given by V = 4x² volt. The electric field at the point (1m, 0, 2m) in V/m is :

8 along positive x-axis

16 along negative x-axis

16 along positive x-axis

8 along negative x-axis

LiveFree JEE Main Previous Year Online Papers Live Free JEE Advance Previous Year Online Papers

College PredictorLive

Know your College Admission Chances Based on your Rank/Percentile, Category and Home State.

Get your JEE Main Personalised Report with Top Predicted Colleges in JoSA

V = 4x²V

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

Here,

\frac{\partial V}{\partial x} = 8 x

and,

\frac{\partial V}{\partial y} = \frac{\partial V}{\partial z} = 0

Hence,

\vec{E} = - 8 x \hat{i}

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

Hence,

\vec{E} = - 8 \hat{i} N / C