JEE Main 2025 · 7 April · morning · Single correct · +4 / −1
The percentage increase in magnetic field (B) when space within a current carrying solenoid is filled with magnesium (magnetic susceptibility χ_(Mg)=1.2 × 10⁻⁵ ) is :
- (a) 5/3 × 10⁻⁵ %
- (b) 5/6 × 10⁻⁴ %
- (c) 5/6 × 10⁻⁵ %
- (d) 6/5 × 10⁻³ %
Answer and solution
Answer (d) 6/5 × 10⁻³ %
Solution
Physics sir · 3 steps
Filling the solenoid multiplies B by (1+χ), so the fractional increase is just χ itself.
- Field without core. With air (vacuum) inside, the field of a long solenoid is B₀ = μ₀ n I.
- Field with magnesium. A material core changes μ₀ to μ = μ₀(1+χ), so B = μ₀(1+χ) n I = (1+χ)B₀.
(B - B₀)/B₀ × 100% = χ × 100% = 1.2 × 10⁻⁵ × 100% = 1.2 × 10⁻³%
- So. Since 1.2 = 6/5, the increase is 6/5 × 10⁻³%, which is option (d). Magnesium is paramagnetic, so the rise is real but very small.
The idea to keep. For any core material, B = (1+χ)B₀. The fractional change in B equals χ; multiply by 100 for the percentage. Positive χ raises B, negative χ lowers it.
Answer from the NTA final answer key. Solution by PrepWiser.