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BITSAT2019PhysicsUnits and DimensionsActual

The dimensional formula of μ 0 ε 0 is

Options

  1. AML 2   T - 3 A 2
  2. BM 0 LT - 1 A 0
  3. CML 2   T - 3 A - 2
  4. DM - 1   L - 2   T 3   A 2

Correct answer

C. ML 2   T - 3 A - 2

Step-by-step solution

We know that, velocity of light c is terms of ϵ 0 and μ 0 is given by c = 1 μ 0 ε 0 ⇒ c 2 = 1 μ 0 ε 0 c 2 = 1 μ 0 2 μ 0 ε 0 ⇒ c = 1 μ 0 μ 0 ε 0 ⇒ μ 0 ε 0 = c μ 0       . . . i Dimension of the magnetic field, B = τ N I A = ML 2   T - 2 A L 2 = MA - 1 T - 2 Again, B = μ 0 n I ∴   μ 0 = B n l = MA - 1 T - 2 L - 1 A = MLA - 2 T - 2 μ 0 = MLA - 2 T - 2       &#1

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