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Question
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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