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

1. 4π ε₀ Q × 10² volt/m
2. 12π ε₀ Q × 10² volt/m
3. 4π ε₀ Q × 10²⁰ volt/m
4. 12π ε₀ Q × 10²² volt/m

Correct answer: 4π ε₀ Q × 10² volt/m

Solution

The electric potential V at a distance r from a charge Q is given by V = Q / (4πε₀r). The electric field E is related to the potential by E = V / r. Substituting r = Q × 10¹¹ / V, we find E = 4π ε₀ Q × 10² volt/m.

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