An electric field $\vec{E} = (\vec{i} 20 + \vec{j} 30) {NC}^{- 1}$ exists in space. If the potential at the origin is taken to be zero, find the potential at (2 m, 2 m).

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Solution

Given:
$\vec{E} = (\vec{i} 20 + \vec{j} 30) N / C$
$\vec{r} = (2 \vec{i} + 2 \vec{j})$
So, $V = - \vec{E} . \vec{r}$
$\Rightarrow V = - (\vec{i} 20 + 30 \vec{j}) . (2 \vec{i} + 2 \vec{j}) \Rightarrow V = - (2 \times 20 + 2 \times 30) = - 100 V$

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