Electromagnetic Induction — JEE Main PYQs

The current ( i ) at time $\mathrm{t}=0$ and $\mathrm{t}=\infty$ respectively for the given circuit is :

A coil of inductance 2 H having negligible resistance is connected to a source of supply whose voltage is given by $\mathrm{V}=3t$ volt. (where $t$ is in second). If the voltage is applied when $t=0$, the energy stored in the coil after 4 s is ____ J.

An aeroplane, with its wings spread 10 m, is flying at a speed of $180\mathrm{km}/\mathrm{h}$ in a horizontal direction. The total intensity of earth's field at that part is $2.5\times 10^{-4}\mathrm{Wb}/{\mathrm{m}}^2$ and the angle of dip is $60^{\circ }$. The emf induc …

A coil is placed in a magnetic field as shown below : $B$
A current is induced in the coil because $\vec{B}$ is:

A small square look offside 'a' and one turn is placed inside a larger square loop of side b and one turn ( $b\gg a$ ). The two loops are coplanar with their centres coinciding. If a current I is passed in the square loop offside ' $b$ ', then the coefficient of mutual induc …

Consider an electrical circuit containing a two way switch '$S$'. Initially $S$ is open and then $T_1$ is connected to $T_2$. As the current in $\mathrm{R}=6\Omega$ attains a maximum value of steady state level, ${\mathrm{T}}_1$ is disconnected from ${\mathrm{T}}_2$ and immed …

An inductor of 10 mH is connected to a 20 V battery through a resistor of $10\mathrm{k}\Omega$ and a switch. After a long time, when maximum current is set up in the circuit, the current is switched off. The current in the circuit after $1\mu \mathrm{s}$ is …

A circular conducting coil of radius 1 m being heated by the change of magnetic field $\vec{B}$ passing perpendicular to the plane in which the coil is laid. The resistance of the coil is $2\mu \Omega$. The magnetic field is slowly switched off such that its magnitude changes in …

In the given figure the magnetic flux through the loop increases according to the relation ${\varphi }_{\beta }(t)10t^2+20t$, where ${\varphi }_{\beta }$ is in milliwebers and t is in seconds. The magnitude of current through $\mathrm{R}=2\Omega$ resistor at …

A square loop of side 20 cm and resistance $1\Omega$ is moved towards right with a constant speed vo.The right arm of the loop is in a uniform magnetic field of 5T. The field is perpendicular to the plane of the loop and is going into it. The loop is connected to a network of re …

For the given circuit the current $i$ through the battery when the key in closed and the steady state has been reached is ______.

A conducting bar of length $L$ is free to slide on two parallel conducting rails as shown in the figure. Two resistors ${\mathrm{R}}_1$ and ${\mathrm{R}}_2$ are connected across the ends of the rails. There is a uniform magnetic field $\vec{B}$ pointing into the page. An …

The magnetic field in a region is given by $\vec{B}=B_0\left(\frac{x}{a}\right)\hat{k}$. A square loop of side d is placed with its edges along the x and y axes. The loop is moved with a constant velocity $\vec{v}=v_0\hat{i}$. The emf induced in the loop is:

The time taken for the magnetic energy to reach $25\%$ of its maximum value, when solenoid of resistance R , inductance L is connected to a battery, is:

A long solenoid of radius $R$ carries a time ($t$) dependent current $I(t)=I_{0}t(1-t)$. A ring of radius 2$R$ is placed coaxially near its middle. During the time interval $0\le t\le 1$, the induced current ($I_R$) and the induced EMF ($V_R$) in the ring changes as:

A loop $ABCDEFA$ of straight edges has six corner points $A(0,0,0),B(5,0,0),C(5,5,0),D(0,5,0),E(0,5,5)$ and $F(0,0,5)$. The magnetic field in this region in $\vec{B}=(3\hat{i}+4\hat{k})T$. The quantity of flux through the loop ABCDEFA (in Wb ) is ____.

An emf of 20 V is applied at time $t=0$ to a circuit containing in series 10 mH inductor and $5\Omega$ resistor. The ratio of the currents at time $t=\infty$ and at $t=40$ s is close to: (take $e^2=7.389$)

A planar loop of wire rotates in a uniform magnetic field. Initially, at $t=0$, the plane of the loop is perpendicular to the magnetic field. If it rotates with a period of 10 s about an axis in its plane then the magnitude of induced emf will be maximum and minimum, respectively …

At time $t=0$ magnetic field of 1000 Gauss is passing perpendicularly through the area defined by the closed loop shown in the figure. If the magnetic field reduces linearly to 500 Gauss, in the next 5s, then induced EMF in the loops is:

As shown in the figure, a battery of emf $\epsilon$ is connected to an inductor $L$ and resistance $R$ in series. The switch is closed at $t=0$. The total charge that flows from the battery, between $t=0$ and $t=t_c$ ($t_c$ is the time constant of the circuit) is

In LC circuit the inductance $\mathrm{L}=40\mathrm{mH}$ and capacitance $\mathrm{C}=100\mu \mathrm{F}$. If a voltage $\mathrm{V}(\mathrm{t})=10\sin (314\mathrm{t})$ is applied to the circuit, the current in the circuit is given as

In a fluorescent lamp choke (a small transformer) 100 V of reverse voltage is produced when the choke current changes uniformly from 0.25 A to 0 in a duration of 0.025 ms. The self-inductance of the choke (in mH) is estimated to be ____.

An infinitely long straight wire carrying current I, one side opened rectangular loop and a conductor C with a sliding connector are located in the same plane, as shown in the figure. The connector has length l and resistance R. It slides to the right with a velocity v . The resi …

An elliptical loop having resistance R, of semi major axis a and semi minor axis b is placed in a magnetic field as shown in the figure. If the loop is rotated about the x-axis with angular frequency $\omega$, the average power loss in the loop due to joule heating is:

A uniform magnetic field $B$ exists in a direction perpendicular to the plane of a square loop made of a metal wire. The wire has a diameter of 4 mm and a total length of 30 cm. The magnetic field changes with time at a steady rate $\frac{dB}{dt}=0.032{\mathrm{Ts}}^{-1}$. The indu …

Two concentric circular coils, $C_1$ and $C_2$ are placed in the XY plane. $C_1$ has 500 turns, and a radius of $1$ cm. $C_2$ has 200 turns and radius of $20$ cm. $C_2$ carries a time dependent current $I(t)=(5t^2-2t+3)$ A where t is in s. The emf induced in $C_1$ (in mV), …

A part of complete circuit is shown in the figure. At some instant, the value of current I is 1 A and it is decreasing at a rate of $10^2{\mathrm{As}}^{-1}$. The value of the potential difference ${\mathrm{V}}_{\mathrm{P}}-{\mathrm{V}}_{\mathrm{Q}}$, (in volts) at that instant, …

A small bar magnet is moved through a coil at constant speed from one end to the other. Which of the following series of observations will be seen on the galvanometer G attached across the coil?

Three positions shown describe:
(a) the magnet's entry
(b) magnet is completely insi …

A series L-R circuit is connected to a battery of emf V. If the circuit is switched on at $t=0$, then the time at which the energy stored in the inductor reaches $(1/n)$ times of its maximum value, is:

A thin strip 10 cm long is on a ∪ shaped wire of negligible resistance and it is connected to a spring of spring constant $0.5{\mathrm{Nm}}^{-1}$ (see figure). The assembly is kept in a uniform magnetic field of 0.1 T. If the strip is pulled from its equilibrium position and relea …

A 20 Henry inductor coil is connected to a 10 ohm resistance in series as shown in figure. The time at which rate of dissipation of energy (Joule's heat) across resistance is equal to the rate at which magnetic energy is stored in the inductor, is

The total number of turns and cross-section area in solenoid is fixed. However, its length L is varied by adjusting the separation between windings. The inductance of solenoid will be proportional to:

A solid metal cube of edge length 2 cm is moving in a positive $y$-direction at a constant speed of $6\mathrm{m}/\mathrm{s}$. There is a uniform magnetic field of 0.1 T in the positive z-direction. The potential difference between the two faces of the cube perpendicular to th …

A copper wire is wound on a wooden frame, whose shape is that of an equilateral triangle. If the linear dimension of each side of the frame is increased by a factor of 3 , keeping the number of turns of the coil per unit length of the frame the same, then self inductance of the c …

The figure shows a square loop L of side 5 cm which is connected to a network of resistances. The whole set up is moving towards right with a constant speed of $1{\mathrm{cms}}^{-1}$. At some instant, a part of L is in a uniform magnetic field of 1 T, perpendicular to the plane of …

A coil of self inductance 10 mH and resistance $0.1\Omega$ is connected through a switch to a battery of internal resistance $0.9\Omega$. After the switch is closed the time taken for the current to attain $80\%$ of the saturation values is: [take $\ln 5=1.6$]

There are two long co-axial solenoids of same length l. The inner and outer coils have radii $r_1$ and $r_2$ and number of turns per unit length $n_1$ and $n_2$ respectively. The ratio of mutual inductance to the self-inductance of the inner-coil is:

In the circuit shown,

The switch ${\mathrm{S}}_1$ is close at time $\mathrm{t}=0$ and the switch $S_2$ is kept open. At some later time ( $t_0$ ), the switch $S_1$ is opened and $S_2$ is closed. The behaviour of the current I as a function of time ' t ' is gi …

In the figure shown, a circuit contains two identical resistors with resistance $\mathrm{R}=5\Omega$ and an inductance with $\mathrm{L}=2\mathrm{mH}$. An ideal battery of 15 V is connected in the circuit. What will be the current through the battery long after the switch is …

Consider the LR circuit shown in the figure. If the switch S is closed at $\mathrm{t}=0$ then the amount of charge that passes through the battery between $t=0$ and $t=\frac{L}{R}$ is :

A 10 m long horizontal wire extends from North East to South West. It is falling with a speed of $5.0{\mathrm{ms}}^{-1}$, at right angles to the horizontal component of the earth's magnetic field, $0.3\times 10^{-4}\mathrm{Wb}/{\mathrm{m}}^2$. The value of the induced em …

Two coils P and Q are separated by some distance. When a current of 3 A flows through coil P a magnetic flux of $10^{-3}\mathrm{Wb}$ passes through Q. No current is passed through Q. When no current passes through P and a current of 2 A passes through Q, the flux through P is:

A very long solenoid of radius $R$ is carrying current $I(t)=kt{e}^{-\alpha t}(k>0)$, as a function of time ( $\mathrm{t}\ge 0$ ). counter clockwise current is taken to be positive. A circular conducting coil of radius 2 R is placed in the equatorial plane of the solenoid and c …

In a coil of resistance $100\Omega$, a current is induced by changing the magnetic flux through it as shown in the figure. The magnitude of change in flux through the coil is:

An inductor ( $\mathrm{L}=0.03\mathrm{H}$ ) and a resistor ( $\mathrm{R}=0.15\mathrm{k}\Omega$ ) are connected in series to a battery of 15 V EMF in a circuit shown. The key ${\mathrm{K}}_1$ has been kept closed for a long time. Then at $\mathrm{t}=0,{\mathrm{K}}_1$ is opene …

An LCR circuit is equivalent to a damped pendulum. In an LCR circuit the capacitor is charged to ${\mathrm{Q}}_0$ and then connected to the L and R as shown.
If a student plots graphs of the square of maximum charge ( ${\mathrm{Q}}_{\text{max }}^2$ ) on the capacitor with time ( …

A conductor lies along the z-axis at $-1.5\le \mathrm{z}<1.5\mathrm{m}$ and carries a fixed current of 10.0 A in $-{\hat{\mathrm{a}}}_{\mathrm{z}}$ direction (see figure). For a field …

In the circuit shown here, the point 'C' is kept connected to point 'A' till the current flowing through the circuit becomes constant. Afterward, suddenly, point 'C' is disconnected from point 'A' and connected to point 'B' at time $t=0$. Ratio of the voltage across resistance an …

A metallic rod of length ' $\ell$ ' is tied to a string of length $2\ell$ and made to rotate with angular speed $\omega$ on a horizontal table with one end of the string fixed. If there is a vertical magnetic field ' B ' in the region, the e.m.f. induced across the ends of …

A circular loop of radius 0.3 cm lies parallel to a much bigger circular loop of radius 20 cm . The centre of the small loop is on the axis of the bigger loop. The distance between their centres is 15 cm . If a current of 2.0 A flows through the smaller loop, then the flux linked …