The space inside a straight current carrying solenoid is filled with a magnetic material having magnetic susceptibility equal to 1.2 × 10⁻⁵. What is fractional increase in the magnetic field inside solenoid with respect to air as medium inside the solenoid?

Solution

Physics sir · 3 steps

With the material inside, B goes from μ₀ n I to μ₀(1+χ)n I, so the extra part is just χ.

1. Field with air. With air inside, take the field as B₀ = μ₀ n I. The susceptibility of air is so small that we treat it as zero.
2. Field with material. The material magnetises and adds its own field. The permeability becomes μ = μ₀(1+χ), so B = μ₀(1+χ) n I.

   (B - B₀)/B₀ = (μ₀(1+χ)nI - μ₀ nI)/(μ₀ nI) = χ

3. So. The fractional increase equals the susceptibility, 1.2 × 10⁻⁵, which is option (a).

The idea to keep. Filling a solenoid with a material multiplies B by (1+χ). So the fractional change in field is χ itself. A positive χ raises the field, a negative one lowers it.

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