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(A) The magnetic field inside an air-cored solenoid is given by $B_0 = \mu_0 n I$.When the solenoid is filled with a magnetic material of relative per

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$1.2 	imes 10^{-5}$

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(A) The magnetic field inside an air-cored solenoid is given by $B_0 = \mu_0 n I$.When the solenoid is filled with a magnetic material of relative permeability $\mu_r$,the magnetic field becomes $B = \mu_0 \mu_r n I$.The magnetic susceptibility $\chi$ is related to relative permeability by the formula $\mu_r = 1 + \chi$.Given $\chi = 1.2 	imes 10^{-5}$,we have $\mu_r = 1 + 1.2 	imes 10^{-5}$.The fractional increase in the magnetic field is given by $\frac{\Delta B}{B_0} = \frac{B - B_0}{B_0} = \frac{\mu_0 \mu_r n I - \mu_0 n I}{\mu_0 n I} = \mu_r - 1$.Substituting $\mu_r = 1 + \chi$,we get $\frac{\Delta B}{B_0} = (1 + \chi) - 1 = \chi$.Therefore,the fractional increase is $1.2 	imes 10^{-5}$.

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