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Question

In a certain region the electric potential at a point $(x, y, z)$ is given by the potential function $V = 2 x + 3 y - z$ . Then the electric field in this region will :

A

increase with increase in x and y

B

increase with increase in y and z

C

increase with increase in z and x

D

remain constant

Medium

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Solution

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Correct option is D)

$V = 2 x + 3 y - z$

$E_{x} = - \frac{d V}{d x} = - 2, E_{y} = - \frac{d V}{d y} = - 3$ and $E_{z} = - \frac{d V}{d z} = 1$

As the field components are independent of x,y and z so the field remains constant.

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