Electromagnetic Induction

The current in a coil of self inductance 2.0 H is increasing according to $I=2\sin\left(t^2\right)$ A. The amount of energy spent during the period when current changes from 0 to 2 A is ______ J.

The magnetic flux through a coil perpendicular to its plane is varying according to the relation $\phi=\left(5t^3+4t^2+2t-5\right)$ Weber. If the resistance of the coil is 5 ohm, then the induced current through the coil at t = 2 s will be,

A $10\ \Omega$, 20 mH coil carrying constant current is connected to a battery of 20 V through a switch. Now after switch is opened current becomes zero in 100 $\mu$s. The average e.m.f. induced in the coil is ______ V.

The dimension of mutual inductance is :

Two coils of self inductance $L_1$ and $L_2$ are connected in series combination having mutual inductance of the coils as M. The equivalent self inductance of the combination will be :

A metallic conductor of length 1 m rotates in a vertical plane parallel to east-west direction about one of its end with angular velocity 5 rad s$^{-1}$. If the horizontal component of earth's magnetic field is $0.2\times10^{-4}$ T, then emf induced between the two ends of the conductor is :

A metallic rod of length 20 cm is placed in North-South direction and is moved at a constant speed of 20 m/s towards East. The horizontal component of the Earth's magnetic field at that place is $4\times10^{-3}$ T and the angle of dip is 45°. The emf induced in the rod is ______ mV.

A coil is placed in a time varying magnetic field. If the number of turns in the coil were to be halved and the radius of wire doubled, the electrical power dissipated due to the current induced in the coil would be :

(Assume the coil to be short circuited.)

A small square loop of wire of side $l$ is placed inside a large square loop of wire L ($L\gg l$). Both loops are coplanar and their centres coincide at point O as shown in figure. The mutual inductance of the system is :

Magnetic flux (in weber) in a closed circuit of resistance 20 $\Omega$ varies with time t(s) as $\phi=8t^2-9t+5$. The magnitude of the induced current at $t=0.25$ s will be ______ mA.

In a coil of resistance 8 Ω, the magnetic flux due to an external magnetic field varies with time as $\phi=\dfrac23\left(9-t^2\right)$. The value of total heat produced in the coil, till the flux becomes zero, will be ______ J.

A conducting circular loop is placed in X - Y plane in presence of magnetic field $\vec B=\left(3t^3\hat j+3t^2\hat k\right)$ in SI unit. If the radius of the loop is 1 m, the induced emf in the loop, at time, t = 2 s is $n\pi$ V. The value of n is ______.

The dimensions of $\left(\dfrac{B^2}{\mu_0}\right)$ will be :

(if $\mu_0$ : permeability of free space and B : magnetic field)

For the given circuit the current through battery of 6 V just after closing the switch 'S' will be ______ A.

A coil of inductance 1 H and resistance 100 Ω is connected to a battery of 6 V. Determine approximately :

(a) The time elapsed before the current acquires half of its steady - state value.

(b) The energy stored in the magnetic field associated with the coil at an instant 15 ms after the circuit is switched on. (Given ln2 = 0.693, $e^{-3/2}$ = 0.25)

A long straight wire carries a current, $I = 2$ ampere. A semi-circular conducting rod is placed beside it on two conducting parallel rails of negligible resistance. Both the rails are parallel to the wire. The wire, the rod and the rails lie in the same horizontal plane, as shown in the figure. Two ends of the semi-circular rod are at distances 1 cm and 4 cm from the wire. At time $t = 0$, the rod starts moving on the rails with a speed $v = 3.0$ m/s (see the figure).

A resistor $R = 1.4\ \Omega$ and a capacitor $C_o = 5.0\ \mu$F are connected in series between the rails. At time $t = 0$, $C_o$ is uncharged. Which of the following statement(s) is(are) correct? [$\mu_0 = 4\pi \times 10^{-7}$ SI units. Take $\ln 2 = 0.7$]

When the dipole $m$ is placed at a distance $r$ from the center of the loop (as shown in the figure), the current induced in the loop will be proportional to

The work done in bringing the dipole from infinity to a distance $r$ from the center of the loop by the given process is proportional to

A light disc made of aluminium (a nonmagnetic material) is kept horizontally and is free to rotate about its axis as shown in the figure. A strong magnet is held vertically at a point above the disc away from its axis. On revolving the magnet about the axis of the disc, the disc will (figure is schematic and not drawn to scale)

The inductors of two $LR$ circuits are placed next to each other, as shown in the figure. The values of the self-inductance of the inductors, resistances, mutual-inductance and applied voltages are specified in the given circuit. After both the switches are closed simultaneously, the total work done by the batteries against the induced $EMF$ in the inductors by the time the currents reach their steady state values is ______ mJ.