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......$V$

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

$A$ 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 $t > 0$?

$A$ long coaxial cable carries current $I$ along its surface. The current flows down the surface of the inner cylinder of radius $a$ and back along the outer cylinder of radius $b$.

$A$ solenoid is connected to a battery so that a steady current flows through it. If an iron core is inserted into the solenoid, then the current in the coil

The self-inductance $(L)$ produced by a solenoid of length '$l$' having '$N$' number of turns and cross-sectional area '$A$' is given by the formula (where $\phi$ = magnetic flux,$\mu_0$ = permeability of vacuum).