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Question
Give the relation between electric field and electric potential.
Solution
Consider a positive charge q kept fixed at the origin. To move a unit positive charge by a small distance dx in the electric field E, the work done is given by dW = -E dx. The minus sign implies that work is done against the electric field. This work done is equal to an electric potential difference. Therefore,
dW = dV.
(or) dV = -Edx
Hence E = `"dV"/"dx"`
The electric field is the negative gradient of the electric potential.
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