JEE MainPhysicsUnits and Dimensions
If E represents electric field, B represents magnetic field and ₀ is the permeability of free space, then the dimensional formula of the expression ( EB ₀ ) is
Options
- A[ M T ⁻³]
- B[ M L ⁻¹ T ⁻²]
- C[ M L ^2 T ⁻³]
- D[ M L ^2 T ⁻²]
Correct answer
A. [ M T ⁻³]
Step-by-step solution
The expression EB ₀ represents the magnitude of the Poynting vector, which is the energy transmitted per unit area per unit time (Intensity of an electromagnetic wave). Intensity = Energy Area Time = Power Area Dimensions of Energy = [ M L ^2 T ⁻²] Dimensions of Area = [ L ^2] Dimensions of Time = [ T ] Therefore, the dimensions of EB ₀ are [ M L ^2 T ⁻²] [ L ^2][ T ] = [ M T ⁻³] . Alternatively, using E = cB , we can write EB ₀ = c ( B^2 ₀ ) . Since B^2 2 ₀ is the magnetic energy density (Energy/Volume), its dimen