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(B) The inductance $L$ of a solenoid is given by the formula $L = \mu_0 n^2 A \ell$,where $n$ is the turn density (turns per unit length),$A$ is the c

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(B) The inductance $L$ of a solenoid is given by the formula $L = \mu_0 n^2 A \ell$,where $n$ is the turn density (turns per unit length),$A$ is the cross-sectional area,and $\ell$ is the length of the solenoid.Given that the turn density $n$ remains constant.The cross-sectional area $A = \pi r^2$. If the radius $r$ is doubled $(r' = 2r)$,the new area $A' = \pi (2r)^2 = 4\pi r^2 = 4A$.The length is halved,so $\ell' = \ell / 2$.Substituting these into the formula for the new inductance $L'$:$L' = \mu_0 n^2 A' \ell' = \mu_0 n^2 (4A) (\ell / 2) = 2 (\mu_0 n^2 A \ell) = 2L$.The percentage increase in inductance is given by $\frac{L' - L}{L} 	imes 100\% = \frac{2L - L}{L} 	imes 100\% = 100\%$.

For a solenoid,keeping the turn density constant,if its length is halved and its cross-sectional radius is doubled,then the inductance of the solenoid increases by.....$\%$

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