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

Options

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

Answer

A

Explanation

The electric potential `V (x,y,z) = 4x^(2)` volt
Now `vecE = - (hati (del V)/(delx) + hatj(delV)/(delx) + hatk(delV)/(delz))`
Now `(delV)/(delx) = 8x, (delV)/(dely) = 0` and `(delV)/(delz) = 0`
Hence `vecE = - 8x hati`, so at point `(1m, 0.2 m)`
`vecE = -8 hati` volt//metre or `8` along negative X-axis