JEE Advanced2015PhysicsUnits and DimensionsActual
In terms of potential difference V , electic current I , permittivity ε 0 , permeability μ 0 and speed of light c , the dimensionally correct equation(s) is (are)
Options
- Aμ 0 I 2 = ε 0 V 2
- Bε 0 I = μ 0 V
- CI = ε 0 c V
- Dμ 0 c I = ε 0 V
Correct answer
A. μ 0 I 2 = ε 0 V 2
Step-by-step solution
Using C = 1 μ 0 ϵ 0 & R = μ 0 ϵ 0 we can check corrections (i) μ 0 I 2 = ϵ 0 V 2 μ 0 ϵ 0 = V 2 I 2 = R 2 ∴ R 2 = R 2 Correct (ii) ϵ 0 I = μ 0 V ϵ 0 μ 0 = V I 1 R 2 = R Not correct (iii) I = ϵ 0 c V 1 V = ϵ 0 c = ϵ 0 μ 0 ϵ 0 1 R = ϵ 0 μ 0 = 1 R Correct (iv) μ 0 C I = ϵ 0 V μ 0 C ϵ 0 = V I μ 0 ϵ 0 1 μ 0 ϵ 0 = R ∴ 1 ϵ 0 μ 0 ϵ 0 = R ⇒ R