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 ?

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$1 .2 \times 10^{- 3}$

$1 .2 \times 10^{- 5}$

$1 .8 \times 10^{- 3}$

$2 .4 \times 10^{- 5}$

answer is A.

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Detailed Solution

$\begin{array}{l} χ = 1 .2 \times 10^{- 5} \\ μ_{r} = 1 + χ = 1 + 1 .2 \times 10^{- 5} \end{array}$

Fractional Change

$\begin{array}{l} = \frac{ΔB}{B} = \frac{μ_{0} μ_{r} ni - μ_{0} ni}{μ_{0} ni} = (μ_{r} - 1) \\ = 1 .2 \times 10^{- 5} \end{array}$

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