The unit of √(2I/(ε₀ c)) is :
(I = intensity of an electromagnetic wave, c = speed of light)

Solution

Physics sir · 4 steps

Recognise the expression: it is just the intensity formula solved for the peak electric field.

1. Intensity formula. The average energy carried per unit area per unit time by an EM wave is related to its peak electric field E₀ by the relation below.

   I = 1/2ε₀ c E₀² ⇒ E₀ = √(2I/(ε₀ c))

2. Unit of the field. So the given expression is an electric field. Electric field is force per unit charge, so its unit is N C⁻¹, which is the same as V m⁻¹.
3. Quick check. I is in W m⁻², ε₀ in C² N⁻¹ m⁻² and c in m s⁻¹. Then 2I/(ε₀ c) has unit (N m s⁻¹ m⁻²)/(C² N⁻¹ m⁻¹ s⁻¹) = N² C⁻², whose square root is N C⁻¹.
4. So. The unit is N C⁻¹, option (b).

The idea to keep. When an odd combination appears in a units question, first ask whether it is a known formula rearranged. Here I = 1/2ε₀ c E₀² turns it into an electric field at once.

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