$A$ coil is wound on a core of rectangular cross-section. If all the linear dimensions of the core are increased by a factor of $2$ and the number of turns per unit length of the coil remains the same, the self-inductance increases by a factor of (Assume, permeability is same).

The total number of turns and cross-section area in a solenoid are fixed. However,its length $L$ is varied by adjusting the separation between windings. The inductance of the solenoid will be proportional to

An air-cored solenoid with $30 \ cm$ length,area of cross-section $25 \ cm^2$,and $500$ turns carries a current of $2.5 \ A$. The current is suddenly switched off in a brief time of $10^{-3} \ s$. How much is the average back emf induced across the ends of the open switch in the circuit (in $V$)? (Ignore the variation in magnetic field near the ends of the solenoid.)

The current in a coil of inductance $5\, H$ decreases at the rate of $2\, A/s$. The induced $e.m.f.$ is....$V$

Current in a circuit falls from $5.0\, A$ to $0\, A$ in $0.1\, s$. If an average $emf$ of $200\, V$ is induced,estimate the self-inductance of the circuit in $H$.

$A$ coil of $100$ turns carries a current of $5\, mA$ and creates a magnetic flux of $10^{-5} \, Wb$. The inductance is.....$mH$.