Self and Mutual Induction

Consider a conducting wire of length $L$ bent in the form of a circle of radius $R$ and another conductor of length $a\left(a<<R\right)$ is bent in the form of a square. The two loops are then placed in same plane such that the square loop is exactly at the centre of the circular loop. What will be the mutual inductance between the two loops?

Two coaxial coils $A$ and $B$ of radii $R_1$ and $R_2$ are placed in the same plane. $\left({\mathrm{R}}_2>R_1\right)$. If a current is passed through coil $B$, the coefficient of mutual inductance between the coils is proportional to

A system consists of two coaxial circular current-carrying rings as shown in the figure. Their self inductances are $L_1$ and $L_2$, respectively, and $M$ is the coefficient of mutual induction. They carry current in the indicated directions. The magnetic energy of the system is,

In an inductor of self-inductance $L=2 \mathrm{mH}$, current changes with time according to relation $i=t^2{e}^{-1}$. At what time $emf$ is zero?

An AC of $50 \mathrm{Hz}$ and $1 \mathrm{A}$ peak value flows in a transformer whose mutual inductance is $1.5 \mathrm{H}$. The induced emf in the secondary is,

Three inductances $L_1=0.75 \mathrm{H}$, $L_2=L_3=0.5 \mathrm{H}$ are connected as shown below. Assuming no coupling, the resultant inductance will be

The mutual inductance of a pair of coils is $0.75 \mathrm{H}$. If the current in the primary coil changes from $0.5 \mathrm{A}$ to $0$ in $0.01 \mathrm{s}$, then the average induced e.m.f. in the secondary coil is

Choke coil works on the principle of

A small square loop of wire of side is placed inside a large square loop of wire of side $L\left(L>>l\right)$. The loops are co-planar and their centres coincide. The mutual inductance of the system is proportional to

A solenoid has $2000$ $\mathrm{turns}$ wound over a length of $0.30 \mathrm{m}$. The area of its cross-section is $1.2\times {10}^{-3} {\mathrm{m}}^2$. Around its central section, a coil of $300$ $\mathrm{turn}$ is wound. If an initial current of $2 \mathrm{A}$ in the solenoid is reversed in $0.25 \mathrm{s},$ then the emf induced in the coil is

A superconducting loop of radius $R$ has self inductance $L$. A uniform and constant magnetic field $B$ is applied perpendicular to the plane of the loop. Initially current in this loop is zero. The loop is rotated by $180°.$ The current in the loop after rotation is equal to-

When the current $i$ in a certain inductor coil is $5.0 \mathrm{A}$ and is increasing at the rate of $10.0 \mathrm{A} {\mathrm{s}}^{-1}$, the potential difference across the coil is $140 \mathrm{V}$. When the current is $5.0 \mathrm{A}$ and decreasing at the rate of $10.0 \mathrm{A} {\mathrm{s}}^{-1}$, the potential difference is $60 \mathrm{V}$. The self inductance of the coil is -

A coil of radius $1 \mathrm{cm}$ and number of turns $100$ is placed in the middle of a long solenoid of radius $5 \mathrm{cm}$ and having $5 \mathrm{turns} {\mathrm{cm}}^{-1}$. The mutual induction in millihenry will be

The energy stored in an electromagnet is $400 \mathrm{mJ}$ when a current $2 \mathrm{A}$ flows in the coils. The self-inductance of the coil is 

A circular coil of radius $5 \mathrm{cm}$ has $500$ turns of a wire. The approximate value of the coefficient of self-induction of the coil will be

The inductance of a closed-packed coil of $400$ turns is $8 \mathrm{mH}$. A current of $5 \mathrm{mA}$ is passed through it. The magnetic flux through each turn of the coil is

A wire of fixed length is wound on a solenoid of length $l$ and radius $r$. Its self-inductance is found to be $L$. Now if the same wire is wound on a solenoid of length $\frac{l}{2}$ and radius $\frac{r}{2}$, then the self inductance will be

Average energy stored in a pure inductance $L$ when a current $i$ flows through it, is

The mutual inductance of a pair of coils is $0.75 \mathrm{H}$. If current in the primary coil changes from $0.5 \mathrm{A}$ to zero in $0.01 \mathrm{s}$, find average induced emf in secondary coil.

The back emf induced in a coil, when current changes from $1 \mathrm{A}$ to zero in $1 \mathrm{ms}$, is $4 \mathrm{V}$, the self-inductance of the coil is