$A$ long solenoid of $N$ turns has a self-inductance $L$ and area of cross-section $A$. When a current $i$ flows through the solenoid,the magnetic field inside it has magnitude $B$. The current $i$ is equal to:

For a toroid,$N = 500$,radius $R = 40 \text{ cm}$,and area of cross-section $A = 10 \text{ cm}^2$. Find the inductance in $\mu\text{H}$.

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

$A$ $30\text{ cm}$ long solenoid has $10$ turns per cm and area of $5\text{ cm}^2$. The current through the solenoid coil varies from $2\text{ A}$ to $4\text{ A}$ in $3.14\text{ s}$. The e.m.f. induced in the coil is $\alpha \times 10^{-5}\text{ V}$. The value $\alpha$ is . . . . . . .

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 self-induced $e.m.f.$ in a $0.1 \, H$ coil when the current in it is changing at the rate of $200 \, A/s$ is......$V$