First slide

Electrostatic potential

Question

In a certain region of space, the potential is given by : $V = K [2 x^{2} - y^{2} + z^{2}]$ The electric field at the point (1,1, 1) has magnitude =

Moderate

A

$K \sqrt{6}$
B

$2 K \sqrt{6}$
C

$2 K \sqrt{3}$
D

$4 K \sqrt{3}$

Solution

$\vec{E} = - \frac{δ V}{δ x} \hat{i} - \frac{δ V}{δ y} \hat{j} - \frac{δ V}{δ z} \hat{k} = - 4 k x \hat{i} + 2 k y \hat{j} - 2 k z \hat{k} A t p o i n t (1, 1, 1), \vec{E} = - 4 k \hat{i} + 2 k \hat{j} - 2 k \hat{k} \Rightarrow |\vec{E}| = 2 \sqrt{6} k$

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