Electrostatics 2 Question 21
22. The electric potential $V$ at any point $x, y, z$ (all in metre) in space is given by $V=4 x^{2}$ volt. The electric field at the point $(1 m, 0,2 m)$ is
(1992, 1M)
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Solution:
- $\quad \mathbf{E}=-\frac{\partial V}{\partial x} \hat{\mathbf{i}}+\frac{\partial V}{\partial y} \hat{\mathbf{j}}+\frac{\partial V}{\partial z} \hat{\mathbf{k}} \Rightarrow V=4 x^{2}$
Therefore, $\frac{\partial V}{\partial x}=8 x$ and $\frac{\partial V}{\partial y}=0=\frac{\partial V}{\partial z}$
$$ \mathbf{E}=-8 x \hat{\mathbf{i}} $$
or $\mathbf{E}$ at $(1 m, 0,2 m)$ is $-8 \hat{\mathbf{i}} V / m$
