JEE Main 2025 · 23 January · morning · Single correct · +4 / −1
The electric flux is φ=α σ+β λ where λ and σ are linear and surface charge density, respectively. (α/β) represents
- (a) displacement
- (b) charge
- (c) electric field
- (d) area
Answer and solution
Answer (a) displacement
Solution
Physics sir · 4 steps
Both terms add up to flux, so they must have the same dimensions. Compare them and the ratio falls out.
- Same dimensions. You can only add quantities of the same kind. So ασ and βλ must have identical dimensions.
[α][σ] = [β][λ] ⇒ [α/β] = [λ]/[σ]
- Put in units. Linear charge density λ is charge per length, in C m⁻¹. Surface charge density σ is charge per area, in C m⁻².
- Take the ratio. λ/σ = (C m⁻¹)/(C m⁻²) = m. The coulombs cancel and one metre is left over.
- So. α/β has the dimension of length, which is the dimension of displacement.
The idea to keep. When terms are added in a formula, each term carries the same dimensions. Equate them and the ratio of the unknown constants comes out directly.
Answer from the NTA final answer key. Solution by PrepWiser.