Electromagnetic Induction — JEE Advanced PYQs

List-I contains four conducting loops lying in the XY plane, as shown in the figures. The loops are rotating about Z axis passing through the point 0 with time period T in clockwise direction. The region $\mathrm{x}>0$ contains a uniform magnetic field B in the +z direction. List …

A conducting square loop initially lies in the $XZ$ plane with its lower edge hinged along the $X$-axis. Only in the region $y\ge 0$, there is a time dependent magnetic field pointing along the $Z$-direction, $\vec{B}(t)=B_0(\cos \omega t)\hat{K}$, where $B_0$ …

A conducting square loop of side $L$, mass $M$ and resistance $R$ is moving in the $XY$ plane with its edges parallel to the $X$ and $Y$ axes. The region $y\ge 0$ has a uniform magnetic field, $\vec{B}=B_{0}k$. The magnetic field is zero everywhere else. At ti …

The circuit shown in the figure contains an inductor $L$, a capacitor $C_0$, a resistor $R_0$ and an ideal battery. The circuit also contains two keys ${\mathrm{K}}_1$ and ${\mathrm{K}}_2$. Initially, both the keys are open and there is no charge on the capacitor. A …

A region in the form of an equilateral triangle (in x-y plane) of height $L$ has a uniform magnetic field $\overrightarrow{\mathrm{B}}$ pointing in the +z-direction. A conducting loop PQR, in the form of an equilateral triangle of the same height $L$, is placed in the $x-y$ plane …

A thin conducting rod MN of mass 20 gm, length 25 cm and resistance $10\Omega$ is held on frictionless, long, perfectly conducting vertical rails as shown in the figure. There is a uniform magnetic field ${\mathrm{B}}_0=4\mathrm{T}$ directed perpendicular to the plane of the r …

A rectangular conducting loop of length 4 cm and width 2 cm is in the $xy$-plane, as shown in the figure. It is being moved away from a thin and long conducting wire along the direction $\frac{\sqrt{3}}{2}\hat{x}+\frac{1}{2}\hat{y}$ with a constant speed $v$. The wire is carryi …

Consider an LC circuit, with inductance $L=0.1H$ and capacitance $C=10^{-3}F$, kept on a plane. The area of the circuit is $1m^2$. It is placed in a constant magnetic field of strength $B_0$ which is perpendicular to the plane of the circuit. At time $t=0$, the m …

A small circular loop of area $A$ and resistance $R$ is fixed on a horizontal $xy$-plane with the center of the loop always on the axis $\hat{n}$ of a long solenoid. The solenoid has $m$ turns per unit length and carries current $I$ counterclockwise as shown in the fi …

A special metal S conducts electricity without any resistance. A closed wire loop, made of S, does not allow any change in flux through itself by inducing a suitable current to generate a compensating flux. The induced current in the loop cannot decay due to its zero resistance. …

A special metal S conducts electricity without any resistance. A closed wire loop, made of S, does not allow any change in flux through itself by inducing a suitable current to generate a compensating flux. The induced current in the loop cannot decay due to its zero resistance. …

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 …

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 …

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, …

A conducting wire of parabolic shape, initially $y=x^2$, is moving with velocity $\vec{V}=V_0\hat{i}$ in a nonuniform magnetic field $\overrightarrow{\mathrm{B}}={\mathrm{B}}_0\left(1+{\left(\frac{\mathrm{y}}{\mathrm{L}}\right)}^{\beta }\right)\hat{\mathrm{k}}$, as shown in fi …

A 10 cm long perfectly conducting wire PQ is moving, with a velocity 1cm/s on a pair of horizontal rails of zero resistance. One side of the rails is connected to an inductor $\mathrm{L}=1\mathrm{mH}$ and a resistance $\mathrm{R}=1\Omega$ as shown in figure. The horizontal …

In the figure below, the switches $S_1$ and $S_2$ are closed simultaneously at $t=0$ and a current starts to flow in the circuit. Both the batteries have the same magnitude of the electromotive force (emf) and the polarities are as indicated in the figure. Ignore mutual induc …

A circular insulated copper wire loop is twisted to form two loops of area $A$ and $2A$ as shown in the figure. At the point of crossing the wires remain electrically insulated from each other. The entire loop lies in the plane (of the paper). A uniform magnetic field …

A source of constant voltage $V$ is connected to a resistance $R$ and two ideal inductors $L_1$ and $L_2$ through a switch $S$ as shown. There is no mutual inductance between the two inductors. The switch $S$ is initially open. At $t=0$, the switch is closed and …

A conducting loop in the shape of a right angled isosceles triangle of height 10 cm is kept such that the 90° vertex is very close to an infinitely long conducting wire (see the figure). The wire is electrically insulated from the loop. The hypotenuse of the triangle is parallel …

Two inductors $L_1$ (inductance 1 mH, internal resistance 3 $\Omega$) and $L_2$ (inductance 2 mH, internal resistance 4 $\Omega$), and a resistor $R$ (resistance 12 $\Omega$) are all connected in parallel across a 5 V battery. The circuit is switched on at time …

A rigid wire loop of square shape having side of length $L$ and resistance $R$ is moving along the $x$-axis with a constant velocity ${\mathrm{v}}_0$ in the plane of the paper. At $t=0$, the right edge of the loop enters a region of length $3L$ where there is a unifo …

Paragraph for Questions 9 and 10

A point charge $Q$ is moving in a circular orbit of radius $R$ in the $x-y$ plane with an angular velocity $\omega$. This can be considered as equivalent to a loop carrying a steady current $\frac{Q\omega }{2\pi }$. A uniform magnetic f …

Paragraph for Questions 9 and 10

A point charge $Q$ is moving in a circular orbit of radius $R$ in the $x-y$ plane with an angular velocity $\omega$. This can be considered as equivalent to a loop carrying a steady current $\frac{Q\omega }{2\pi }$. A uniform magnetic f …

A circular wire loop of radius $R$ is placed in the $x-y$ plane centered at the origin $O$. A square loop of side $a(a\ll R)$ having two turns is placed with its center at $z=\sqrt{3}R$ along the axis of the circular wire loop, as shown in figure. The plane of the squ …

A current carrying infinitely long wire is kept along the diameter of a circular wire loop, without touching it. The correct statement(s) is(are)

A long circular tube of length 10 m and radius 0.3 m carries a current $I$ along its curved surface as shown. A wire-loop of resistance 0.005 ohm and of radius 0.1 m is placed inside the tube with its axis coinciding with the axis of the tube. The current varies as …

Two metallic rings A and B, identical in shape and size but having different resistivities ${\rho }_A$ and ${\rho }_B$, are kept on top of two identical solenoids as shown in the figure. When current $I$ is switched on in both the solenoids in identical manner, the rings A an …

The figure shows certain wire segments joined together to form a coplanar loop. The loop is placed in a perpendicular magnetic field in the direction going into the plane of the figure. The magnitude of the field increases with time. $I_1$ and $I_2$ are the currents in th …

Column I gives certain situations in which a straight metallic wire of resistance $R$ is used and Column II gives some resulting effects. Match the statements in Column I with the statements in Column II and indicate your answer by darkening appropriate bubbles in the 4 × 4 mat …

STATEMENT-1
A vertical iron rod has a coil of wire wound over it at the bottom end. An alternating current flows in the coil. The rod goes through a conducting ring as shown in the figure. The ring can float at a certain height above the coil.
because
STATEMENT-2
In the above sit …

The capacitor of capacitance C can be charged (with the help of a resistance R) by a voltage source V, by closing switch ${\mathrm{S}}_1$ while keeping switch ${\mathrm{S}}_2$ open. The capacitor can be connected in series with an inductor 'L' by closing switch …

The capacitor of capacitance C can be charged (with the help of a resistance R) by a voltage source V, by closing switch ${\mathrm{S}}_1$ while keeping switch ${\mathrm{S}}_2$ open. The capacitor can be connected in series with an inductor 'L' by closing switch …

Match the following Columns
| (C) Co …