Electromagnetic Induction · Physics · MHT CET

The total charge induced in a conducting loop when it is moved in a uniform magnetic field depends on

A copper ring is held horizontally and a bar magnet is dropped through the ring with its length along the axis of the ring. The acceleration of the falling magnet while it is passing through the ring is

A coil of resistance $400 \Omega$ is placed in ${ }^3$ magnetic field. If the magnetic flux ' $\phi$, ( Wb ) linked with the coil varies with time ' $t$ ' ( $s$ ) ${ }^{\text {is }} \phi=50 \mathrm{t}^2+4$, the current in the coil at $\mathrm{t}=2 \mathrm{~s}$ will be

A coil is wound on a core of rectangular crosssection. If all the linear dimensions of core are increased by a factor 3 and number of turns per unit length of coil remains same, the selfinductance increases by a factor

What is the phase difference between the flux linked with a coil rotating in a uniform magnetic field and the induced e.m.f. produced in it?

Two coils $P$ and $Q$ are kept near each other. When no current flows through coil $P$ and current increases in coil Q at the rate of $10 \mathrm{~A} / \mathrm{S}$, the e.m.f. in coil P is 15 mV . When coil Q carries no current and current of 1.8 A flows through coil $P$, the magnetic flux linked with coil Q is

To manufacture a solenoid of length ' $l$ ' and inductance ' $L$ ', the length of the thin wire required is (Diameter of the solenoid is very less than length, $\mu_0=$ permeability of free space)

Initially a rectangular coil with length vertical is moving out with constant velocity ' $v$ ' in a constant magnetic field ' $B$ ' towards right. Now the same coil is rotated through $90^{\circ}$ in same plane in same magnetic field B and the coil is moving with same velocity $\mathbf{v}$. The magnitude of induced e.m.f. is now

A simple pendulum with bob of mass m and conducting wire of length $L$ swings under gravity through an angle $\theta$. The component of earth's magnetic field in the direction perpendicular to swing is B . Maximum e.m.f. induced across the pendulum is ( $\mathrm{g}=$ acceleration due to gravity)

Three inductances are connected as shown in the figure. The equivalent inductance between A and b is

The current flowing through an inductor of selfinductance L is continuously increasing at constant rate. The variation of induced e.m.f. (e) verses $\mathrm{dI} / \mathrm{dt}$ is shown graphically by figure

The coefficient of mutual induction is 2 H and induced e.m.f. across secondary is 2 kV . Current in the primary is reduced from 6 A to 3 A . The time required for the change of current is

Two planar concentric rings of metal wire having radii $\mathrm{r}_1$ and $\mathrm{r}_2\left(\mathrm{r}_1>\mathrm{r}_2\right)$ are placed in air. The current I is flowing through the coil of larger radius. The mutual inductance between the coils is given by ( $\mu_0=$ permeability of free space)

Out of the following which law obeys the law of conservation of energy?

The magnetic flux through a coil is $4 \times 10^{-4} \mathrm{~Wb}$ at time $t=0$. It reduces to $30 \%$ of its original value in time $t$ second. If e.m.f. induced in the coil is 0.56 mV then the value of $t$ is

A circular coil of resistance ' $R$ ', area ' $A$ ', number of turns ' N ' is rotated about its vertical diameter with angular speed ' $\omega$ ' in a uniform magnetic field of magnitude ' $B$ '. The average power dissipated in a complete cycle is

A coil is wound on a core of rectangular crosssection. If all the linear dimensions of the core are increased by a factor 2 and number of turns per unit length of coil remains same, the self inductance increases by a factor of (Assume, permeability is same)

A graph of magnetic flux $(\phi)$ versus current (I) is shown for 4 different inductors $\mathrm{P}, \mathrm{Q}, \mathrm{R}, \mathrm{S}$. Minimum value of inductance is for inductor

The mutual inductance of two coils is 45 mH . The self-inductance of the coils are $\mathrm{L}_1=75 \mathrm{mH}$ and $\mathrm{L}_2=48 \mathrm{mH}$. The coefficient of coupling between the two coils is

A coil of resistance $250 \Omega$ is placed in a magnetic field. If the magnetic flux $(\phi)$ linked with the coil varies with time $t(\mathrm{~s})$ as $\phi=50 \mathrm{t}^2+7$. The current in the coil at $t=4 \mathrm{~s}$ is

A metal disc of radius R rotates with an angular velocity $\omega$ about an axis perpendicular to its plane passing through its centre in a magnetic field of induction B acting perpendicular to the plane of the disc. The induced e.m.f. between the rim and axis of the disc is

An air cored coil has a self inductance 0.1 H . A soft iron core of relative permeability 1000 is introduced and the number of turns is reduced $\left(\frac{1}{10}\right)^{\text {th }}$. The value of self inductance is

When the number of turns in a coil are made 3 times without any change in the length of the coil, its self inductance becomes

Two solenoids of equal number of turns have their lengths as well as radii in the same ratio $1: 3$. The ratio of their self inductance will be

If number of turns per unit length in a solenoid is tripled, the self inductance of solenoid will

The number of turns in the primary of a transformer are 1000 and in secondary 3000. If 80 V a.c. is applied to the primary, the potential difference per turn of the secondary coil is

A closely wound coil of 100 turns and of crosssection $1 \mathrm{~cm}^2$ has coefficient of self inductance 1 mH . The magnetic induction at the centre of the core of a coil when a current of 2 A flows in it, will be (in $\mathrm{Wb} / \mathrm{m}^2$ )

When the number of turns in a coil is doubled without any change in the length of the coil, its self-inductance

The coefficient of mutual induction is 2 H and induced e.m.f. across secondary is 2 kV Current in the primary is reduced from 6 A to 3 A . The time required for the change of current is

If current of 4 A produces magnetic flux of $3 \times 10^{-3} \mathrm{~Wb}$ through a coil of 400 turns, the energy stored in the coil will be

Two concentric circular coils having radii ' $r_1{ }^{\prime}$ and ' $r_2$ ' $\left(r_2 \ll r_1\right)$ are placed co-axially with centres coinciding. The mutual inductance of the arrangement is ( $\mu_0=$ permeability of free space) (Both coils have single turn)

An inductor coil of inductance $L$ is divided into two parts and both parts are connected in parallel. The net inductance is

Two coils have a mutual inductance 0.003 H . The current changes in the first coil according to equation $I=I_0 \sin \omega t$, where $I_0=8 \mathrm{~A}$ and $\omega=100 \pi \mathrm{rad} \mathrm{s}^{-1}$. The maximum value of e.m.f. in the second coil is

The current in LR circuit if reduced to half What will be the energy stored in it?

Two coils of self-inductance 25 mH and 9 mH are placed close together such that the effective flux in one coil is completely linked with the other The mutual inductance between these coils is

Consider the following circuit. By keeping $\mathrm{S}_1$ closed, the capacitor is fully charged and then $S_1$ is opened and $S_2$ is closed, then

A square loop ABCD is moving with constant velocity ' $\vec{v}$ ' in a uniform magnetic field ' $\vec{B}$ ' which is perpendicular to the plane of paper and directed outward. The resistance of coil is ' $R$ ', then the rate of production of heat energy in the loop is [ L - length of side of loop]

A metal rod of length ' $l$ ' rotates about one of its ends in a plane perpendicular to a magnetic field of induction ' $B$ '. If the e.m.f. induced between the ends of the rod is ' $e$ ', then the number of revolutions made by the rod per second is

Two coils have a mutual inductance $5 \times 10^{-3} \mathrm{H}$. The current changes in the first coil according to the equation $I_1=I_0 \sin \omega t$ where $I_0=10 \mathrm{~A}$ and $\omega=100 \pi \mathrm{rad} / \mathrm{s}$. What is the value of the maximum e.m.f. in the coil?

The magnetic flux through a coil of resistance ' $R$ ' changes by an amount ' $\Delta \phi$ ' in time ' $\Delta t$ '. The amount of induced current and induced charge in the coil are respectively

The planar concentric rings of metal wire having radii $r_1$ and $r_2$ (with $r_1>r_2$ ) are placed in air. The current $I$ is flowing through the coil of larger radius. The mutual inductance between the coils is given by ( $\mu_0=$ permeability of free space)

A magnetic field of $2 \times 10^{-2} \mathrm{~T}$ acts at right angles to a coil of area $100 \mathrm{~cm}^2$ with 50 turns, The average e.m.f. induced in the coil is 0.1 V , when it is removed from the field in time $t$. The value of ' $t$ ' is (in second)

A current of 0.5 A is passed through winding of a long solenoid having 400 turns. The magnetic flux linked with each turn is $3 \times 10^{-3} \mathrm{~Wb}$. The self inductance of the solenoid is

A square loop of area $25 \mathrm{~cm}^2$ has a resistance of $10 \Omega$. The loop is placed in uniform magnetic field of magnitude 40 T . The plane of loop is perpendicular to the magnetic field. The work done in pulling the loop out of the magnetic field slowly and uniformly in 1 second, will be

A graph of magnetic flux $(\phi)$ versus current ( 1 ) is shown for four inductors A, B, C, D. Smaller value of self inductance is for inductor

A circular coil of resistance $R$, area $A$, number of turns ' $N$ ' is rotated about its vertical diameter with angular speed ' $\omega$ ' in a uniform magnetic field of magnitude ' $B$ '. The average power dissipated in a complete cycle is

Two coils are kept near each other. When no current passess through first coil and current in the $2^{\text {nd }}$ coil increases at the rate $10 \mathrm{~A} / \mathrm{s}$, the e.m.f. in the $1^{\mathbb{P}}$ coil is 20 mV . When no current passes through $2^{\text {nd }}$ coil and 3.6 A current passes through $1^2$ coil the flux linkage in coil 2 is

A rod of length ' $l$ ' is rotated with angular velocity ' $\omega$ ' about its one end, perpendicular to a magnetic field of induction ' $B$ '. The e.m.f. induced in the rod is

In an a. c. generator, when the plane of the coil is perpendicular to the magnetic field

An air cored coil has self inductance of 0.1 H . A soft iron core of relative permeability 1000 is introduced and the number of turns is reduced to $\left(\frac{1}{10}\right)^{\text {th }}$. The value of self inductance is now

The coil and magnet are moved in the same direction with same speed (V). The induced e.m.f. is

The magnetic energy stored in an inductor of inductance $5 \mu \mathrm{H}$ carrying a current of 2 A is

A bicycle wheel of radius ' $R$ ' has ' $n$ ' spokes. It is rotating at the rate of ' $F$ ' r.p.m. perpendicular to the horizontal component of earth's magnetic field $\vec{B}$. The e.m.f. induced between the rim and the centre of the wheel is

A long solenoid has 1500 turns. When a current of $$3.5 \mathrm{~A}$$ flows through it, the magnetic flux linked with each turn of solenoid is $$2.8 \times 10^{-3}$$ weber. The self-inductance of solenoid is

A coil having effective area A, is held with its plane normal to magnetic field of induction B. The magnetic induction is quickly reduced by $$25 \%$$ of its initial value in 2 second. Then the e.m.f. induced across the coil will be

The self induction (L) produced by solenoid of length '$$l$$' having '$$\mathrm{N}$$' number of turns and cross sectional area '$$A$$' is given by the formula ($$\phi=$$ magnetic flux, $$\mu_0=$$ permeability of vacuum)

A magnetic field of $$2 \times 10^{-2} \mathrm{~T}$$ acts at right angles to a coil of area $$100 \mathrm{~cm}^2$$ with 50 turns. The average e.m.f. induced in the coil is $$0.1 \mathrm{~V}$$, when it is removed from the field in time '$$t$$'. The value of '$$t$$' is

The alternating e.m.f. induced in the secondary coil of a transformer is mainly due to

A metal disc of radius $$R$$ rotates with an angular velocity $$\omega$$ about an axis perpendicular to its plane passing through its centre in a magnetic field of induction $$B$$ acting perpendicular to the plane of the disc. The magnitude of induced emf between the rim and axis of the disc is

A conductor $$10 \mathrm{~cm}$$ long is moves with a speed $$1 \mathrm{~m} / \mathrm{s}$$ perpendicular to a field of strength $$1000 \mathrm{~A} / \mathrm{m}$$. The emf induced in the conductor is (Given : $$\mu_0=4 \pi \times 10^{-7} \mathrm{~Wb} / \mathrm{Am}$$ )

Three coils of inductance $$\mathrm{L}_1=2 \mathrm{H}, \mathrm{L}_2=3 \mathrm{H}$$ and $$\mathrm{L}_3=6 \mathrm{H}$$ are connected such that they are separated from each other. To obtain the effective inductance of 1 henry, out of the following combinations as shown in figure, the correct one is

The magnet is moved towards the coil with speed '$$\mathrm{V}$$'. The induced e.m.f. in the coil is '$$\mathrm{e}$$'. The magnet and the coil move away from one another each moving with speed '$$\mathrm{V}$$'. The induced e.m.f. in the coil is

A transformer has 20 turns in the primary and 100 turns in the secondary coil. An ac voltage of $$\mathrm{V}_{\text {in }}=600 \sin 314 \mathrm{t}$$ is applied to primary terminal of transformer. Then maximum value of secondary output voltage obtained in volt is

SI units of self inductance is

An air craft of wing span $$40 \mathrm{~m}$$ files horizontally in earth's magnetic field $$5 \times 10^{-5} \mathrm{~T}$$ at a speed of $$500 \mathrm{~m} / \mathrm{s}$$. The e.m.f. generated between the tips of the wings of the air craft is

Inductance per unit length near the middle of a long solenoid is $$\left(\mu_0=\right.$$ permeability of free space, $$\mathrm{n}=$$ number of turns per unit length, $$\mathrm{d}=$$ the diameter of the solenoid)

Two inductors of $$60 \mathrm{~mH}$$ each are joined in parallel. The current passing through this combination is $$2.2 \mathrm{~A}$$. The energy stored in this combination of inductors in joule is

Two coils have a mutual inductance of $$0.004 \mathrm{~H}$$. The current changes in the first coil according to equation $$\mathrm{I}=\mathrm{I}_0 \sin \omega \mathrm{t}$$, where $$\mathrm{I}_0=10 \mathrm{~A}$$ and $$\omega=50 ~\pi \mathrm{~rad} ~\mathrm{s}^{-1}$$. The maximum value of e.m.f. in the second coil in volt is

The magnetic flux through a circuit of resistance '$$R$$' changes by an amount $$\Delta \phi$$ in the time $$\Delta t$$. The total quantity of electric charge '$$Q$$' which passes during this time through any point of the circuit is

The self inductance '$$L$$' of a solenoid of length '$$l$$' and area of cross-section '$$\mathrm{A}$$', with a fixed number of turns '$$\mathrm{N}$$' increases as

A coil having effective area '$$A$$' is held with its plane normal to a magnitude field of induction '$$\mathrm{B}$$'. The magnetic induction is quickly reduced to $$25 \%$$ of its initial value in 1 second. The e.m.f. induced in the coil (in volt) will be

A coil of radius '$$r$$' is placed on another coil (whose radius is $$\mathrm{R}$$ and current flowing through it is changing) so that their centres coincide $$(\mathrm{R} \gg \mathrm{r})$$. If both the coils are coplanar then the mutual inductance between them is ( $$\mu_0=$$ permeability of free space)

When a current of $$1 \mathrm{~A}$$ is passed through a coil of 100 turns, the flux associated with it is $$2.5 \times 10^{-5} \mathrm{~Wb} /$$ turn. The self inductance of the coil in millihenry is

The mutual inductance of a pair of coils, each of '$$N$$' turns, is '$$M$$' henry. If a current of '$$I$$' ampere in one of the coils is brought to zero in '$$t$$' second, the e. m. f. induced per turn in the other coil in volt is

To manufacture a solenoid of length $$1 \mathrm{~m}$$ and inductance $$1 \mathrm{~mH}$$, the length of thin wire required is

(cross - sectional diameter of a solenoid is considerably less than the length)

A hollow metal pipe is held vertically and bar magnet is dropped through it with its length along the axis of the pipe. The acceleration of the falling magnet is ( $$\mathrm{g}=$$ acceleration due to gravity)

Two concentric circular coils having radii $$r_1$$ and $$r_2\left(r_2 << r_1\right)$$ are placed co-axially with centres coinciding. The mutual induction of the arrangement is (Both coils have single turn, $$\mu_0=$$ permeability of free space)

A graph of magnetic flux $$(\phi)$$ versus current (I) is plotted for four inductors A, B, C, D. Larger value of self inductance is for inductor

A square loop of area $$25 \mathrm{~cm}^2$$ has a resistance of $$10 \Omega$$. This loop is placed in a uniform magnetic field of magnitude $$40 \mathrm{~T}$$. The plane of loop is perpendicular to the magnetic field. The work done in pulling the loop out of the magnetic field slowly and uniformly in one second, will be

Two conducting circular loops of radii '$$R_1$$' and '$$R_2$$' are placed in the same plane with their centres coinciding. If $$R_1>R_2$$, the mutual inductance $$M$$ between them will be directly proportional to

If current '$$I$$' is flowing in the closed circuit with collective resistance '$$R$$', the rate of production of heat energy in the loop as we pull it along with a constant speed '$$\mathrm{V}$$' is ( $$\mathrm{L}=$$ length of conductor, $$\mathrm{B}=$$ magnetic field)

Two coils $$\mathrm{A}$$ and $$\mathrm{B}$$ have mutual inductance 0.008 $$\mathrm{H}$$. The current changes in the coil A, according to the equation $$\mathrm{I}=\mathrm{I}_{\mathrm{m}} \sin \omega \mathrm{t}$$, where $$\mathrm{I}_{\mathrm{m}}=5 \mathrm{~A}$$ and $$\omega=200 \pi ~\mathrm{rad} ~\mathrm{s}^{-1}$$. The maximum value of the e.m.f. induced in the coil $$B$$ in volt is

The mutual inductance (M) of the two coils is $$3 ~\mathrm{H}$$. The self inductances of the coils are $$4 ~\mathrm{H}$$ and $$9 ~\mathrm{H}$$ respectively. The coefficient of coupling between the coils is

The magnetic flux through a loop of resistance $$10 ~\Omega$$ varying according to the relation $$\phi=6 \mathrm{t}^2+7 \mathrm{t}+1$$, where $$\phi$$ is in milliweber, time is in second at time $$\mathrm{t}=1 \mathrm{~s}$$ the induced e.m.f. is

An electron (mass $$\mathrm{m}$$ ) is accelerated through a potential difference of '$$V$$' and then it enters in a magnetic field of induction '$$B$$' normal to the lines. The radius of the circular path is ($$\mathrm{e}=$$ electronic charge)

A conducting wire of length $$2500 \mathrm{~m}$$ is kept in east-west direction, at a height of $$10 \mathrm{~m}$$ from the ground. If it falls freely on the ground then the current induced in the wire is (Resistance of wire $$=25 \sqrt{2} \Omega$$, acceleration due to gravity $$\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2, \mathrm{~B}_{\mathrm{H}}=2 \times 10^{-5} \mathrm{~T}$$ )

Self inductance of solenoid is

The magnetic flux through a coil of resistance '$$R$$' changes by an amount '$$\Delta \phi$$' in time '$$\Delta \mathrm{t}$$'. The total quantity of induced electric charge '$$\mathrm{Q}$$' is

Self inductance of a solenoid cannot be increased by

A graph of magnetic flux $$(\phi)$$ versus current (I) is drawn for four inductors A, B, C, D. Larger value of self inductance is for inductor.

A current 'I' produces a magnetic flux '$$\phi$$' per turn in a coil of '$$n$$' turns. Self inductance of the coil is '$$L$$'. The relation between them is

A current $$I=10 \sin (100 \pi t)$$ ampere, is passed in a coil which induces a maximum emf $$5 \pi$$ volt in neighbouring coil. The mutual inductance of two coils is

A rectangular loop $$\mathrm{PQMN}$$ with movable arm $$\mathrm{PQ}$$ of length $$12 \mathrm{~cm}$$ and resistance $$2 \Omega$$ is placed in a uniform magnetic field of $$0.1 \mathrm{~T}$$ acting perpendicular to the plane of the loop as shown in figure. The resistances of the arms MN, NP and MQ are negligible. The current induced in the loop when arm PQ is moved with velocity $$20 \mathrm{~ms}^{-1}$$ is

A coil has an area $$0.06 \mathrm{~m}^2$$ and it has 600 turns. After placing the coil in a magnetic field of strength $$5 \times 10^{-5} \mathrm{Wbm}^{-2}$$, it is rotated through $$90^{\circ}$$ in 0.2 second. The magnitude of average e.m.f induced in the coil is

$$\left[\cos 0^{\circ}=\sin 90^{\circ}=1 \text { and } \sin 0^{\circ}=\cos 90^{\circ}=0\right]$$

. If the current of '$$I$$' A gives rise to a magnetic flux '$$\phi$$' through a coil having '$$N$$' turns then mangetic energy stored in the medium surrounding the coil is

A conducting loop of resistance 'R' is moved to magnetic field, the total induced charge depends upon

The self inductance of solenoid of length $$31.4 \mathrm{~cm}$$, area of cross section $$10^{-3} \mathrm{~m}^2$$ having total number of turns 500 will be nearly [$$\mu_0=4 \pi \times 10^{-7}$$ SI unit]

A circuit has self-inductance 'L' H and carries a current 'I' A. To prevent sparking when the circuit is switched off, a capacitor which can withstand 'V' volt is used. The least capacitance of the capacitor connected across the switch must be equal to

Eddy currents are produced when

The magnitude of flux linked with coil varies with time as $$\phi=3 t^2+4 t+7$$. The magnitude of induced e.m.f. at $$t=2 \mathrm{~s}$$ is

At what rate a single conductor should cut the magnetic flux so that current of $$1.5 \mathrm{~mA}$$ flows through it when a resistance of $$5 \Omega$$ is connected across its ends?

the magnetic flux (in weber) in a closed circuit of resistance $$20 \Omega$$ varies with time $$t$$ second according to equation $$\phi=5 t^2-6 t+9$$. The magnitude of induced current at $$t=0.2$$ second is

A circular coil of radius '$$R$$' has '$$N$$' turns of a wire. The coefficient of self induction of the coil will be ( $$\mu_0=$$ permeability of free space)

A wire of length 1 m is moving at a speed of 2 m/s perpendicular homogenous magnetic field of 0.5 T. The ends of the wire are joined to resistance 6$$\Omega$$. The rate at which work is being done to keep the wire moving at that speed is

The magnetic potential energy stored in a certain inductor is $$25 \mathrm{~mJ}$$, when the current in the inductor is $$50 \mathrm{~mA}$$. This inductor is of inductance

A wire of length '$$L$$'; having resistance '$$R$$' falls from a height '$$\ell$$' in earth's horizontal magnetic field '$$B$$'. The current through the wire is ( $$\mathrm{g}=$$ acceleration due to gravity)

A coil of radius '$$\mathrm{r}$$' is placed on another coil (whose radius is '$$\mathrm{R}$$' and current through it is changing) so that their centres coincide. ( $$R > r$$ ). If both coplanar, then the mutual inductance between them is proportional to

A metal wire of length $$2500 \mathrm{~m}$$ is kept in east-west direction, at a height of $$10 \mathrm{~m}$$ from the ground. If it falls freely on the ground then the current induced in the wire is (Resistance of wire $$=25 \sqrt{2} \Omega, \mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2$$ and Earth's horizontal component of magnetic field $$\left.\mathrm{B}_{\mathrm{H}}=2 \times 10^{-5} \mathrm{~T}\right)$$

Two conducting wire loops are concentric and lie in the same plane. The current in the outer loop is clockwise and increasing with time. The induced current in the inner loop is

A straight conductor of length 0.6 M is moved with a speed of 10 ms$$^{-1}$$ perpendicular to magnetic field of induction 1.2 weber m$$^{-2}$$. The induced e.m.f. across the conductor is

Metal rings $P$ and $Q$ are lying in the same plane, where current I is increasing steadily. The induced current in metal rings is shown correctly in figure

The length of solenoid is $$I$$ whose windings are made of material of density $$D$$ and resistivity $$\rho$$. The winding resistance is $$R$$. The inductance of solenoid is [$$m=$$ mass of winding wire, $$\mu_0=$$ permeability of free space]

A coil of $$n$$ turns and resistance $$R \Omega$$ is connected in series with a resistance $$\frac{R}{2}$$. The combination is moved for time $$t$$ second through magnetic flux $$\phi_1$$ to $$\phi_2$$. The induced current in the circuit is

2. Two coils have a mutual inductance of 0.01 H . The current in the first coil changes according to equation, $I=5 \sin 200 \pi t$. The maximum value of emf induced in the second coil is