If the electric potential at any point (x, y, z)m in space is given by V = 3 x ^ 2 volt. The electric field at the point (1, 0, 3)m will be :

JEE Main 202229 JuneEvening Shift

Exam: JEE Main
Year: 2022
Date: 29 June
Shift: Evening Shift
Subject: Physics
Chapter: Electrostatics

JEE Main 2022 · 29 June · Evening Shift · Physics · Electrostatics

If the electric potential at any point (x, y, z)m in space is given...

If the electric potential at any point

\left(x, y, z\right)m

in space is given by

V = 3{x}^{2}

volt. The electric field at the point

\left(1, 0, 3\right)m

will be :

Options

A $3{Vm}^{- 1}$ , directed along positive $x$ -axis.
B $3{Vm}^{- 1}$ , directed along negative $x$ -axis.
C $6{Vm}^{- 1}$ , directed along negative $x$ -axis.
D $6{Vm}^{- 1}$ , directed along positive $x$ -axis.

Correct answer

C. $6{Vm}^{- 1}$ , directed along negative $x$ -axis.

Step-by-step solution

Electric potential $V = 3{x}^{2}$

Electric potential and electric field are related as $E = - \dfrac{d V}{d x} = - 6x$ .

At the point \left(1, 0, 3\right)m $, </p><p>$ ⇒ E = - 6 \times 1 = - 6V{m}^{- 1} $</p><p>Thus, electric field is$ 6V{m}^{- 1} $along negative$ x ‐ axis.

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