JEE MainPhysicsUnits and Dimensions
The dimensional formula of the expression E B ₀ is (where E is the electric field, B is the magnetic field and ₀ is the permeability of free space)
Options
- A[ML^2T⁻³]
- B[MT⁻³]
- C[ML⁻¹T⁻²]
- D[MLT⁻²]
Correct answer
B. [MT⁻³]
Step-by-step solution
The expression E B ₀ represents the magnitude of the Poynting vector, which is the energy crossing per unit area per unit time (Intensity). Alternatively, using the relation E = cB (where c is the speed of light in vacuum), we can write: E B ₀ = c ( B^2 ₀ ) The term B^2 ₀ has the dimensions of magnetic energy density (Energy per unit volume). [ B^2 ₀ ] = [ML^2T⁻²] [L^3] = [ML⁻¹T⁻²] The speed of light c has dimensions [LT⁻¹] . Therefore, the dimensions of E B ₀ are: [LT⁻¹] [ML⁻¹T⁻²] = [MT⁻³] Answer: [MT⁻³]