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If μ₀ and ε₀ are the permeability and permittivity of free space, respectively, then the dimension of 1/(μ₀ε₀) is

Asked in JEE Main 2nd April 2nd Shift 2025 · Impedance, dimensions and radar

(1) (L²)/(T²)
(2) L/(T²)
(3) (T²)/(L²)
(4) (T²)/L

Answer: (1) (L²)/(T²)

Step-by-step solution

c = 1/√μ₀ε₀ ⇒ 1/(μ₀ε₀) = c²

[c²] = (L T⁻¹)² = L²/T²

Why the other options are wrong

(2) L/T² is an acceleration; 1/(μ₀ε₀) is the square of a speed
(3) T²/L² is the dimension of μ₀ε₀ itself — you forgot to invert
(4) T²/L is neither — the length exponent was not squared

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