The electric potential at a point (x,y,z) is given by V = – x²y – xz³ + 4. The electric field E⃗ at that point is

Options

(a) E⃗ = i 2xy + j (x² + y²) + k (3xz – y²)
(b) E⃗ = i z³ + j xyz + kz²
(c) E⃗ = i (2xy – z³) + j xy² + k 3z² x
(d) E⃗ = i (2xy + z³) + j x² + k 3xz²

Correct Answer:

E⃗ = i (2xy + z³) + j x² + k 3xz²

Explanation:

The electric field at a point is equal to negative of potential gradient at that point.
E⃗ = – ?V/ ?r = [ -?V/ ?x i – ?V/ ?y j – ?V/ ?z k ]
E⃗ = i (2xy + z³) + j x² + k 3xz²