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Question
An electric field \[\vec{E} = \vec{i}\] Ax exists in space, where A = 10 V m−2. Take the potential at (10 m, 20 m) to be zero. Find the potential at the origin.
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Solution
Given:
Electric field intensity,
\[\vec{E} = \hat{ i } \text{Ax} = 10\text{ x } \hat{i} \]
Potential,
\[dV = - \vec{E} . \vec{\text{dx}} = - 10\text{xdx}\]
On integrating, we get
\[V = 10 \times \frac{x^2}{2} = - \left[ 5 x^2 \right]_{10}^0 \]
\[V = 5 \times 100 = 500 \] V
So, at the origin, the potential is 500 V.
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