Electromagnetic induction

A coil of an area $2 {\mathrm{m}}^2$ is placed in a magnetic field which changes from $4 \mathrm{Wb}/{\mathrm{m}}^2$ to $8 \mathrm{Wb}/{\mathrm{m}}^2$ in $2$ seconds. Find the induced e.m.f. in the coil.

Two identical co-axial loops carry a current ‘$i$’ each circulating in the same direction. If loops approach each other then correct statement (s) is/are :

Magnetic flux linked with a stationary loop of resistance $4 \mathrm{\Omega }$ varies with time as $\varphi =3t\left(2-t\right)$. (In Wb). The amount of heat generated in joules during $t=0$ to $t=2 \mathrm{s}$ is

A conducting $L$-shape rod $ABC$ is rotated with uniform angular speed $\omega$ in uniform magnetic field $B_0$ with the help of two equal string about an axis shown In the figure. Potential $A,B,C$ and $D$ is $V_A,V_B,V_C$ and $V_D$ respectively. ($OA=OC=AB=BC=l$, magnetic field $={\mathrm{B}}_0$) ($D$ is mid point of $AB$) match the following ($\overrightarrow{\omega }$ is directed opposite to $\overrightarrow{B}$)

Two circular coils $P$ & $Q$ are coaxially & carry currents $I_1$ and $I_2$ respectively (all direction are w.r.t. the observer)

The diagram shows a circular non-conducting smooth fixed track kept concentric to a magnetic field of magnitude $B$ which exists in a cylindrical region of radius $r\left(r>R\right)$. There is small bead of mass $m$ and charge $q$ rests on the track. The bead can move freely along track. If the magnetic field is switched off then

Uniform magnetic field $\mathrm{B}=-{\mathrm{B}}_0\hat{\mathrm{k}}$ present from $\mathrm{X}=0$ to $\mathrm{X}=\mathrm{l}$. A super conducting loop of given side length $\mathrm{I}$ and self inductance $\mathrm{L}$ start with speed ${\mathrm{v}}_0$ with no initial current choose correct options. (Mass of loop is $\mathrm{m}$)

Two long parallel horizontal rails, a distance $d$ apart and each having a resistance $\lambda$ per unit length, are joined at one end by a resistance $R$. A perfectly conducting rod $\mathrm{MN}$ of mass $m$ is free to slide along the rails without friction (shown in figure). There is a uniform magnetic field of induction $B$ normal to the plane of the paper and directed into the paper. A variable force $F$ is applied to the rod $\mathrm{MN}$ such that, as the rod moves, a constant current I flows through $R$. Let the applied force $F$ be expressed as function of the distance $x$ of the rod from $R$, and be given by $F=p+q\lambda +r{\lambda }^2$, where $p,q,r$ are functions of other variables. Find the exponent (power) of $I$ in the product $p$ $qr$.

In the figure, a toroidal coil $S_1$ of a rectangular cross-section containing $N$ loops.
Its inner and outer radii are $a,b$, respectively. The height of the torus is also $a$
A thin conducting ring, $S_2$ encircles the turns, and carries a time dependent current, $I\left(t\right)=I_0{e}^{-t/t}$
Where$I_0$ and $\tau$ are constants and $R$ is resistance of coil.

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A uniform disc of radius $R$ having charge $Q$ distributed uniformly all over its surface is placed on a smooth horizontal surface. A magnetic field, $B=kx{t}^2$, where $k$ is a constant $x$ is the distance (in metre) from the centre of the disc and $t$ is the time (in second), is switched on perpendicular to the plane of the disc. Find the torque (in $N-m$) acting on the disc after $15\sec$. (Take $4\mathrm{kQ}=2.50$ S.I. unit and $R=1\mathrm{m}$).

In the diagram shown, a uniform magnetic field is present perpendicular to the plane of the paper. Both the rings are identical and have a constant resistance per unit length. The left ring has been kept fixed at its position and the right ring is slide uniformly on the left ring towards the right hand side. Which of the following statements is/are true?

Will the earth’s magnetic field induce any current in the metallic surface of an artificial satellite when it is orbiting around the poles?

The primary winding of transformer has $500$ turns whereas its secondary has 5000 turns. The primary is connected to an ac supply of $20 \mathrm{V},$ $50 \mathrm{Hz}.$ The secondary will have an output of :-

If a coil of metal wire is kept stationary in a uniform magnetic field, then _____.

The law of electromagnetic induction has been used in the construction of

If the magnetic flux is expressed in weber, then the magnetic induction can be expressed in 

A thin non-conducting ring of mass $m$ and radius $a$ carrying a charge $q$ can rotate freely about its own axis which is vertical. At the initial moment the ring was at rest in horizontal position and no magnetic field was present. At instant $t=0$, a uniform magnetic field is switched on which is vertically downward and increases with time according to the law $B=B_{0}t$. Neglecting magnetism induced due to rotational motion of ring.

Angular acceleration of the ring is:

Two concentric coplanar circular loops made of wire, with resistance per unit length ${10}^{-4} \mathrm{\Omega } {\mathrm{m}}^{-1}$, have diameters $0.2 \mathrm{m}$ and $2 \mathrm{m}$. A time-varying potential difference $\left(4+2.5t\right) \mathrm{V}$ is applied to the large loop. Calculate the current in the smaller loop (in $A$).

(Answer to two decimal places)

In the circuit, a battery of emf $E$, resistance $R$ and inductance coils $L_1$ and $L_2$ and switch $s$ are connected as shown in the figure. Initially, the switch is open.
  

Two parallel resistanceless rails are connected by an inductor of inductance $\mathrm{L}$ at one end as shown in figure. A magnetic filed $\mathrm{B}$ exists in the space which is perpendicular to the plane of the rails. Now a conductor of length $\mathrm{l}$ and mass $\mathrm{m}$ is placed transverse on the rail and given an impulse $\mathrm{J}$ toward the rightward direction. Then choose the correct options(s).