JEE Main 2023 · 11 April · morning · Single correct · +4 / −1
The free space inside a current carrying toroid is filled with a material of susceptibility 2 × 10⁻². The percentage increase in the value of magnetic field inside the toroid will be
- (a) 0.1%
- (b) 1%
- (c) 2%
- (d) 0.2%
Answer and solution
Answer (c) 2%
Solution
Physics sir · 3 steps
Filling the toroid multiplies B by 1 + χ, so the fractional rise is just χ itself.
- H stays fixed. The field intensity H = nI depends only on the winding and the current, so filling the core does not change it. Only the medium's response changes B.
B₀ = μ₀ H, B = μ₀ (1 + χ) H
- Fractional increase. (B - B₀)/B₀ = (μ₀ χ H)/(μ₀ H) = χ = 2 × 10⁻².
- So. As a percentage, 2 × 10⁻² × 100 = 2%, which is option (c).
The idea to keep. When a core fills a solenoid or toroid at fixed current, B goes up by the factor μᵣ = 1 + χ. The fractional change in B is just χ.
Answer from the NTA final answer key. Solution by PrepWiser.