Consider a long solenoid of length $l$ and radius $r$. If $n$ is the number of turns per unit length and $\mu_0$ is the permeability of free space, the inductance of the solenoid is:

$A$ hollow cylinder has length $l$,radius $r$,and thickness $d$,where $l >> r >> d$,and is made of a material with resistivity $\rho$. $A$ time-varying current $I$ flows through the cylinder in the tangential direction. Assume the current is always uniformly distributed along the length of the cylinder. The cylinder is fixed so that it cannot move; assume that there are no externally generated magnetic fields during the time considered for the problems below. Assume current at $t = 0$ to be $I_0$. What is the current $I(t)$ for $t > 0$?

The ratio of the number of turns per unit length of two solenoids $A$ and $B$ is $1: 3$ and the lengths of $A$ and $B$ are in the ratio $1: 2$. If the two solenoids have the same cross-sectional area,the ratio of the self-inductances of the solenoids $A$ and $B$ is

The self-inductance of a coil is $5 \, H$. If a current of $1 \, A$ changes to $2 \, A$ within $5 \, s$ through the coil,the magnitude of the induced $e.m.f.$ will be $... \, V$.

Two coils $A$ and $B$ have $180$ and $360$ turns respectively. $A$ current of $1 \text{ A}$ flows through both the coils. Due to a current of $1 \text{ A}$ in coil $A$, a flux per turn of $0.8 \times 10^{-3} \text{ Wb}$ is linked with coil $A$. Due to a current of $1 \text{ A}$ in coil $B$, a flux per turn of $1 \times 10^{-3} \text{ Wb}$ is linked with coil $B$. The self-inductance of coil $A$ is $L_A$ and the self-inductance of coil $B$ is $L_B$. The ratio $L_A$ to $L_B$ is:

$A$ solenoid has a length of $1 \,m$ and a cross-sectional area of $0.02 \,m^2$. If the number of turns in the solenoid is $5000$, then the self-inductance of the solenoid is: (in $\pi \,H$)