The space inside a straight current carrying solenoid is filled with a magnetic material having magnetic susceptibility equal to $$1.2 \times 10^{-5}$$. What is fractional increase in the magnetic field inside solenoid with respect to air as medium inside the solenoid?

The magnetic susceptibility of the material inside the solenoid is $$\chi_m = 1.2 \times 10^{-5}$$.

Write the magnetic field with and without the magnetic material.

With air (vacuum): $$B_0 = \mu_0 nI$$

With the magnetic material: $$B = \mu_0(1 + \chi_m) nI$$

Calculate the fractional increase in magnetic field.

$$\frac{\Delta B}{B_0} = \frac{B - B_0}{B_0} = \frac{\mu_0(1 + \chi_m)nI - \mu_0 nI}{\mu_0 nI}$$

$$\frac{\Delta B}{B_0} = (1 + \chi_m) - 1 = \chi_m = 1.2 \times 10^{-5}$$

The fractional increase in the magnetic field is equal to the magnetic susceptibility, which is $$1.2 \times 10^{-5}$$.

The correct answer is Option A.