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The electric potential at a point in free space due to a charge Q coulomb is Q x 10¹¹ v

The electric potential at a point in free space due to a charge Q coulomb is Q x 10¹¹ volts. The electric field at that point is

Options

(a) 4π?￢ﾂﾀQ x 10²² volt/m
(b) 12π?￢ﾂﾀQ x 10²⁰ volt/m
(c) 4π?￢ﾂﾀQ x 10²⁰ volt/m
(d) 12π?￢ﾂﾀQ x 10²² volt/m

Correct Answer:

4π?￢ﾂﾀQ x 10²² volt/m

Explanation:

Given that V = Q x 10¹¹ volts Electric potential at point is given by
V = 1 / 4π?￢ﾂﾀ . Q/r or,
Q x 10¹¹ = 1 / 4π?￢ﾂﾀ . Q/r
r = 1 / 4π?￢ﾂﾀ.10⁻¹¹ m.
As |E| = |V| / r = Q x 10¹¹ / (1 / 4π?￢ﾂﾀ.10⁻¹¹)
= 4π?￢ﾂﾀQ x 10²² volt/m

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