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  • The space inside a straight current carrying solenoid is filled with a magnetic material having magnetic susceptibility equal to <img alt="\mathrm{1.2 \times 10^{-5}}" src="/latex-image/?%5Cma

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

Option: 1

\mathrm{1.2 \times 10^{-5}}


Option: 2

\mathrm{1.2 \times 10^{-3}}


Option: 3

\mathrm{1.8 \times 10^{-3}}


Option: 4

\mathrm{2.4 \times 10^{-5}}


Answers (1)

best_answer

\overrightarrow{B}_1=\mu_{0}\eta i\: [without\: materiel]
\overrightarrow{B }_2=\mu ni\: \left [ with\: material \right ]
and  \mathrm{\mu =\mu _{0}\left ( 1+\lambda \right )}
\mathrm{\lambda \rightarrow susceptibility}
So fraction increase
$$ \begin{aligned} =\frac{B_{2}-B_{1}}{B_{1}} &=\frac{\mu_0(1+\lambda ) n i-\mu_0 n i}{\mu_0 n i} \\ &=\lambda =1.2 \times 10^{-5} \end{aligned}
Hence option 1 correct.

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