The percentage increase in magnetic field ( $B$ ) when space within a current carrying solenoid is f

Question

The percentage increase in magnetic field ( $B$ ) when space within a current carrying solenoid is filled with magnesium (magnetic susceptibility $\chi_{M g}=1.2 	imes 10^{-5}$ ) is\

Professor PC Thomas Classes · Answer

(b) : In the absence of magnesium, $B_{	ext {old }}=\mu_{0} n i$\ In the presence of magnesium, $B_{	ext {new }}=\mu n i$ Increase in magnetic field induction $$ =B_{\mathrm{new}}-B_{\mathrm{old}}=\left(\mu-\mu_{0}ight) n i $$ $\%$ change in $B=\frac{B_{	ext {new }}-B_{	ext {old }}}{B_{	ext {old }}} 	imes 100 \%$\ $=\frac{\left(\mu-\mu_{0}ight) n i}{\mu_{0} n i} 	imes 100 \%=\frac{\left(\mu-\mu_{0}ight)}{\mu_{0}} 	imes 100 \%$\ $=\frac{\left(\mu_{0} \mu_{r}-\mu_{0}ight)}{\mu_{0}} 	imes 100 \%=\left(\mu_{r}-1ight) 	imes 100 \%$\ $\chi_{\mathrm{Mg}} 	imes 100 \%=1.2 	imes 10^{-3} \%$ or $\frac{6}{5} 	imes 10^{-3} \%$\