Question

The dimension of 1/2 ε₀E², where ε₀ is permittivity of free space and E is electric field, is

(A) [L^-2 M¹ T²] 

(B) [L¹ M¹T^-2] 

(C) [L² M¹ T²] 

(D) [L¹ M¹ T¹]

Answer 1

Answer is (B) [L¹ M¹T^-2]

[ε₀E²] = [ε₀] [E]² 

= [M^-1 L^-3 T⁴ A²] [M¹ L¹ T^-3 A^-1]² 

= [M¹ L¹ T^-2 A⁰] 

OR 

\(\frac{1}{2}\)ε₀E² = u

where u is energy density and has dimensions [M¹ L¹ T^-2]