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Derivation of relation E=-dV/dr

Answer»

As you know, standard formula of electric field intensity and potential are given by
E = KQ/r² , V = KQ/r , here Q is the charge , r is the distance between charge and observation point .
V = KQ/r
differentiate with respect to r
dV/dr = -KQ/r² = -E
dV = -E.dr or, E = -dV/dr
Hence, relation between Electric field intensity and potential is E = -∆V/∆r
Here negative sign shows that on uniform electric field intensity if distance increases then potential difference decreases.



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