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Question

Physics Question on Electrostatics

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

A

3 Vm-1, directed along positive x -axis

B

3 Vm-1, directed along negative x -axis

C

6 Vm-1, directed along positive x -axis

D

6 Vm-1, directed along negative x -axis

Answer

6 Vm-1, directed along negative x -axis

Explanation

Solution

The correct answer is (D) : 6 Vm–1, directed along negative x -axis
E⃗=−dVdxi^\vec{E} = - \frac{dV}{dx} \hat{i}
E⃗=−6xi^\vec{E} = - 6x\hat{i}
So,
E⃗\vec{E} at (1, 0 , 3) is
E⃗=−6i^\vec{E} = -6\hat{i} V/m