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If the electric potential is expressed as V = Q × 10¹¹ volts and is also defined by V = 1/(4πε₀) × Q/r, then which of the following correctly represents the value of r?

1. r = 1/(4πε₀) × 10⁻¹¹ m
2. Since |E| = |V|/r, it equals Q × 10¹¹/(4πε₀ × 10⁻¹¹)
3. E = 4πε₀ × Q × 10²² volt m⁻¹
4. None of the above

Correct answer: r = 1/(4πε₀) × 10⁻¹¹ m

Solution

From the given equation, V = Q × 10¹¹ = (1/(4πε₀)) × Q/r, solving for r gives r = 1/(4πε₀) × 10⁻¹¹ m. This matches option A.

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