If ε₀ denotes the permittivity of free space and Φ_E is the flux of the electric field through the area bounded by the closed surface, then dimensions of (ε₀ (d φ_E)/(d t)) are that of :

Solution

Physics sir · 3 steps

This is Maxwell's displacement current, so it must carry the units of current.

1. Recognise the term. Maxwell added i_d = ε₀ dΦ_E/dt to Ampere's law as the displacement current. It sits in the law right next to the conduction current i_c, so it must have the same dimensions.

   ∮ B⃗· dl⃗ = μ₀(i_c + ε₀dΦ_E/dt)

2. Check with Gauss. Gauss's law gives Φ_E = q/ε₀, so ε₀ Φ_E has the units of charge. Dividing by time then gives charge per second, which is current.
3. So. ε₀ dΦ_E/dt has the dimensions [A] of electric current, which is option (c).

The idea to keep. Terms that are added together in an equation must share dimensions. ε₀Φ_E is a charge, so its rate of change is a current.

Answer from the NTA final answer key. Solution by PrepWiser.