Two coaxial solenoids of radii $r_1$ and $r_2$ ($r_2 > r_1$) have the same length $l$ and the same number of turns $N$. If the current in the outer solenoid changes at a rate of $\frac{dI}{dt}$, what is the induced emf in the inner solenoid?

Two coils are placed close to each other. The mutual inductance of the pair of coils depends upon

Two coils of self inductances $2\,\,mH$ and $8\,\,mH$ are placed so close together that the effective flux in one coil is completely linked with the other. The mutual inductance between these coil is

A square loop of side $a$ and resistance $R$ is placed in a spatially uniform magnetic field $B$ that is perpendicular to its plane. The magnetic field decays exponentially with time according to $B(t) = B_0e^{-t/au}$. What is the total charge that flows through the loop from $t=0$ to $t=\infty$?

The self inductance of a coil is $5\,\,henry$, a current of $1\,\,amp$ change to $2\,\,amp$ within $5\,\,second$ through the coil. The value of induced e.m.f. will be

${\rm{2}}\,{\rm{m}}$ long wire is moved with a velocity ${\rm{1}}\,\,{\rm{m}}{{\rm{s}}^{ - 1}}$ in a magnetic field of intensity $0.5\,\,{\rm{Wb}}{{\rm{m}}^{ - 2}}$ in direction perpendicular to the field. The emf induced in it will be

What should be the value of self inductance of an inductor that should be connected to ${\rm{220}}\,{\rm{V}}$, ${\rm{50}}\,{\rm{Hz}}$ supply so that a maximum current of ${\rm{0}}.{\rm{9}}\,{\rm{A}}$ flows through it?

If $100 \, mJ$ of energy is stored in an inductor when $200 \, mA$ of current flows through it, what is its inductance?

A long solenoid has $500$ turns and is $1$ m long. If the magnetic field at the center is $2\pi imes 10^{-4}$ T, what is the current flowing through the solenoid?

Two identical coaxial circular coils, each of radius $R$ and $N$ turns, are placed a distance $d$ apart, where $d << R$. A current $I$ flows through both coils in the same direction. A small circular loop of radius $r$ ($r << R$) and resistance $\rho$ is placed coaxially midway between the coils. If the current in the larger coils is now varied at a rate of $\frac{dI}{dt}$, what is the induced current in the small loop?

If the number of turns in a coil becomes doubled, then it self inductance will be