The electric potential V at any point x, y, z (all in meters) in space is given by `V=4x^2` volts. The electric field at the point (1m, 0, 2m) is……………..`V//m`.

Options

A. 8 along positive X-axis
B. 16 along negative X-axis
C. 16 along positive X-axis
D. 8 along negative X-axis

Answer

D

Explanation

Given `V = 4 x^(2)`
`(del V)/(del x) = 8x , (del V)/(del y) = 0` and `(del V)/(del z) = 0`
As `vec(E) = -[(del V)/(del x) hat(i) (del V)/(del y) hat(j) (del V)/(del z) hat(k)]`
`:. Vec(E) = -[8x hat(i) + 0 + 0] = -8xx1 hat(i) = -8 hat(i) V//m`