Which of the following physical quantities have the same dimensions?

Solution

Physics sir · 2 steps

Write each quantity in SI units first. Matching units means matching dimensions.

1. Electric displacement. D⃗ = ε₀ E⃗, and by Gauss's law ε₀ E = σ near a charged sheet. So D is measured in C m⁻², the same unit as surface charge density.

   Option	First quantity	Second quantity	Same?
   (a)	D: C m⁻² = [L⁻²TA]	σ: C m⁻² = [L⁻²TA]	yes
   (b)	I_d: A = [A]	E: N C⁻¹ = [MLT⁻³A⁻¹]	no
   (c)	J: A m⁻² = [L⁻²A]	σ: C m⁻² = [L⁻²TA]	no, extra T
   (d)	V: J C⁻¹ = [ML²T⁻³A⁻¹]	U: J = [ML²T⁻²]	no

2. So. Only (a) gives two quantities with identical dimensions, [L⁻²TA].

The idea to keep. Electric displacement D = ε₀ E is just charge per unit area, C m⁻². Remember the units of D, J and σ side by side; examiners love pairing them.

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