Electromagnetic Induction · Physics · JEE Main

A coil of area A and N tums is rotating with angular velocity to in a uniform magnetic field $\vec{B}$ about an axis perpendicular to $\vec{B}$. Magnetic flux $\varphi$ and induced emf $\varepsilon$ across it, at an instant when $\vec{B}$ is parallel to the plane of coil, are :

Consider I₁ and I₂ are the currents flowing simultaneously in two nearby coils 1 & 2, respectively. If L₁ = self inductance of coil 1, M₁₂ = mutual inductance of coil 1 with respect to coil 2, then the value of induced emf in coil 1 will be :

A uniform magnetic field of 0.4 T acts perpendicular to a circular copper disc 20 cm in radius. The disc is having a uniform angular velocity of 10 $ \pi $ rad s^-1 about an axis through its centre and perpendicular to the disc. What is the potential difference developed between the axis of the disc and the rim? $(\pi=3.14)$

Regarding self-inductance:

A. The self-inductance of the coil depends on its geometry.

B. Self-inductance does not depend on the permeability of the medium.

C. Self-induced e.m.f. opposes any change in the current in a circuit.

D. Self-inductance is electromagnetic analogue of mass in mechanics.

E. Work needs to be done against self-induced e.m.f. in establishing the current.

Choose the correct answer from the options given below:

A rectangular metallic loop is moving out of a uniform magnetic field region to a field free region with a constant speed. When the loop is partially inside the magnate field, the plot of magnitude of induced emf $(\varepsilon)$ with time $(t)$ is given by

A square loop of side $$15 \mathrm{~cm}$$ being moved towards right at a constant speed of $$2\mathrm{~cm} / \mathrm{s}$$ as shown in figure. The front edge enters the $$50 \mathrm{~cm}$$ wide magnetic field at $$t=0$$. The value of induced emf in the loop at $$t=10 \mathrm{~s}$$ will be :

In a coil, the current changes from $$-2 \mathrm{~A}$$ to $$+2 \mathrm{~A}$$ in $$0.2 \mathrm{~s}$$ and induces an emf of $$0.1 \mathrm{~V}$$. The self inductance of the coil is :

Two conducting circular loops A and B are placed in the same plane with their centres coinciding as shown in figure. The mutual inductance between them is:

A coil is places perpendicular to a magnetic field of $$5000 \mathrm{~T}$$. When the field is changed to $$3000 \mathrm{~T}$$ in $$2 \mathrm{~s}$$, an induced emf of $$22 \mathrm{~V}$$ is produced in the coil. If the diameter of the coil is $$0.02 \mathrm{~m}$$, then the number of turns in the coil is:

Match List I with List II

Choose the correct answer from the options given below:

Match List I with List II

Choose the correct answer from the options given below:

A rectangular loop of length $$2.5 \mathrm{~m}$$ and width $$2 \mathrm{~m}$$ is placed at $$60^{\circ}$$ to a magnetic field of $$4 \mathrm{~T}$$. The loop is removed from the field in $$10 \mathrm{~sec}$$. The average emf induced in the loop during this time is

Given below are two statements: one is labelled as Assertion $$\mathbf{A}$$ and the other is labelled as Reason $$\mathbf{R}$$

Assertion A: A bar magnet dropped through a metallic cylindrical pipe takes more time to come down compared to a non-magnetic bar with same geometry and mass.

Reason R: For the magnetic bar, Eddy currents are produced in the metallic pipe which oppose the motion of the magnetic bar.

In the light of the above statements, choose the correct answer from the options given below

Given below are two statements:

Statement I : If the number of turns in the coil of a moving coil galvanometer is doubled then the current sensitivity becomes double.

Statement II : Increasing current sensitivity of a moving coil galvanometer by only increasing the number of turns in the coil will also increase its voltage sensitivity in the same ratio

In the light of the above statements, choose the correct answer from the options given below :

An emf of $$0.08 \mathrm{~V}$$ is induced in a metal rod of length $$10 \mathrm{~cm}$$ held normal to a uniform magnetic field of $$0.4 \mathrm{~T}$$, when moves with a velocity of:

Certain galvanometers have a fixed core made of non magnetic metallic material. The function of this metallic material is

The induced emf can be produced in a coil by

A. moving the coil with uniform speed inside uniform magnetic field

B. moving the coil with non uniform speed inside uniform magnetic field

C. rotating the coil inside the uniform magnetic field

D. changing the area of the coil inside the uniform magnetic field

Choose the correct answer from the options given below:

A coil is placed in magnetic field such that plane of coil is perpendicular to the direction of magnetic field. The magnetic flux through a coil can be changed :

A. By changing the magnitude of the magnetic field within the coil.

B. By changing the area of coil within the magnetic field.

C. By changing the angle between the direction of magnetic field and the plane of the coil.

D. By reversing the magnetic field direction abruptly without changing its magnitude.

Choose the most appropriate answer from the options given below :

Spherical insulating ball and a spherical metallic ball of same size and mass are dropped from the same height. Choose the correct statement out of the following

{Assume negligible air friction}

A square loop of area 25 cm$$^2$$ has a resistance of 10 $$\Omega$$. The loop is placed in uniform magnetic field of magnitude 40.0 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 1.0 sec, will be

Find the mutual inductance in the arrangement, when a small circular loop of wire of radius '$$R$$' is placed inside a large square loop of wire of side $$L$$ $$(L \gg R)$$. The loops are coplanar and their centres coincide :

A wire of length 1m moving with velocity 8 m/s at right angles to a magnetic field of 2T. The magnitude of induced emf, between the ends of wire will be __________.

A metallic rod of length 'L' is rotated with an angular speed of '$$\omega$$' normal to a uniform magnetic field 'B' about an axis passing through one end of rod as shown in figure. The induced emf will be :

A conducting circular loop of radius $$\frac{10}{\sqrt\pi}$$ cm is placed perpendicular to a uniform magnetic field of 0.5 T. The magnetic field is decreased to zero in 0.5 s at a steady rate. The induced emf in the circular loop at 0.25 s is :

The electric current in a circular coil of 2 turns produces a magnetic induction B₁ at its centre. The coil is unwound and in rewound into a circular coil of 5 tuns and the same current produces a magnetic induction B₂ at its centre. The ratio of $${{{B_2}} \over {{B_1}}}$$ is

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

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.)

Two coils of self inductance L₁ and L₂ 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 $$\times$$ 10^$$-$$4 T, then emf induced between the two ends of the conductor is :

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

A conducting bar moves on two conducting rails as shown in the figure. A constant magnetic field B exists into the page. The bar starts to move from the vertex at time t = 0 with a constant velocity. If the induced EMF is E ∝ tⁿ, then value of n is _________.

The current in an inductor is given by $$\mathrm{I}=(3 \mathrm{t}+8)$$ where $$\mathrm{t}$$ is in second. The magnitude of induced emf produced in the inductor is $$12 \mathrm{~mV}$$. The self-inductance of the inductor _________ $$\mathrm{mH}$$.

The magnetic flux $$\phi$$ (in weber) linked with a closed circuit of resistance $$8 \Omega$$ varies with time (in seconds) as $$\phi=5 t^2-36 t+1$$. The induced current in the circuit at $$t=2 \mathrm{~s}$$ is __________ A.

A small square loop of wire of side $$l$$ is placed inside a large square loop of wire of side $$L\left(L=l^2\right)$$. The loops are coplanar and their centers coincide. The value of the mutual inductance of the system is $$\sqrt{x} \times 10^{-7} \mathrm{H}$$, where $$x=$$ _________.

A ceiling fan having 3 blades of length $$80 \mathrm{~cm}$$ each is rotating with an angular velocity of 1200 $$\mathrm{rpm}$$. The magnetic field of earth in that region is $$0.5 \mathrm{G}$$ and angle of dip is $$30^{\circ}$$. The emf induced across the blades is $$\mathrm{N} \pi \times 10^{-5} \mathrm{~V}$$. The value of $$\mathrm{N}$$ is _________.

A horizontal straight wire $$5 \mathrm{~m}$$ long extending from east to west falling freely at right angle to horizontal component of earths magnetic field $$0.60 \times 10^{-4} \mathrm{~Wbm}^{-2}$$. The instantaneous value of emf induced in the wire when its velocity is $$10 \mathrm{~ms}^{-1}$$ is _________ $$\times 10^{-3} \mathrm{~V}$$.

A square loop of side $$10 \mathrm{~cm}$$ and resistance $$0.7 \Omega$$ is placed vertically in east-west plane. A uniform magnetic field of $$0.20 T$$ is set up across the plane in north east direction. The magnetic field is decreased to zero in $$1 \mathrm{~s}$$ at a steady rate. Then, magnitude of induced emf is $$\sqrt{x} \times 10^{-3} \mathrm{~V}$$. The value of $$x$$ is __________.

Two coils have mutual inductance $$0.002 \mathrm{~H}$$. The current changes in the first coil according to the relation $$\mathrm{i}=\mathrm{i}_0 \sin \omega \mathrm{t}$$, where $$\mathrm{i}_0=5 \mathrm{~A}$$ and $$\omega=50 \pi$$ rad/s. The maximum value of emf in the second coil is $$\frac{\pi}{\alpha} \mathrm{~V}$$. The value of $$\alpha$$ is _______.

An insulated copper wire of 100 turns is wrapped around a wooden cylindrical core of the cross-sectional area $$24 \mathrm{~cm}^{2}$$. The two ends of the wire are connected to a resistor. The total resistance in the circuit is $$12 ~\Omega$$. If an externally applied uniform magnetic field in the core along its axis changes from $$1.5 \mathrm{~T}$$ in one direction to $$1.5 ~\mathrm{T}$$ in the opposite direction, the charge flowing through a point in the circuit during the change of magnetic field will be ___________ $$\mathrm{mC}$$.

A conducting circular loop is placed in a uniform magnetic field of $$0.4 \mathrm{~T}$$ with its plane perpendicular to the field. Somehow, the radius of the loop starts expanding at a constant rate of $$1 \mathrm{~mm} / \mathrm{s}$$. The magnitude of induced emf in the loop at an instant when the radius of the loop is $$2 \mathrm{~cm}$$ will be ___________ $$\mu \mathrm{V}$$.

A metallic cube of side $$15 \mathrm{~cm}$$ moving along $$y$$-axis at a uniform velocity of $$2 \mathrm{~ms}^{-1}$$. In a region of uniform magnetic field of magnitude $$0.5 \mathrm{~T}$$ directed along $$z$$-axis. In equilibrium the potential difference between the faces of higher and lower potential developed because of the motion through the field will be _________ mV.

The magnetic field B crossing normally a square metallic plate of area $$4 \mathrm{~m}^{2}$$ is changing with time as shown in figure. The magnitude of induced emf in the plate during $$\mathrm{t}=2 s$$ to $$\mathrm{t}=4 s$$, is __________ $$\mathrm{mV}$$.

A square loop of side $$2.0 \mathrm{~cm}$$ is placed inside a long solenoid that has 50 turns per centimetre and carries a sinusoidally varying current of amplitude $$2.5 \mathrm{~A}$$ and angular frequency $$700 ~\mathrm{rad} ~\mathrm{s}^{-1}$$. The central axes of the loop and solenoid coincide. The amplitude of the emf induced in the loop is $$x \times 10^{-4} \mathrm{~V}$$. The value of $$x$$ is __________.

$$ \text { (Take, } \pi=\frac{22}{7} \text { ) } $$

A 1 m long metal rod XY completes the circuit as shown in figure. The plane of the circuit is perpendicular to the magnetic field of flux density 0.15 T. If the resistance of the circuit is 5$$\Omega$$, the force needed to move the rod in direction, as indicated, with a constant speed of 4 m/s will be ____________ 10$$^{-3}$$ N.

Two concentric circular coils with radii $$1 \mathrm{~cm}$$ and $$1000 \mathrm{~cm}$$, and number of turns 10 and 200 respectively are placed coaxially with centers coinciding. The mutual inductance of this arrangement will be ___________ $$\times 10^{-8} \mathrm{H}$$. (Take, $$\pi^{2}=10$$ )

As per the given figure, if $$\frac{\mathrm{dI}}{\mathrm{dt}}=-1 \mathrm{~A} / s$$ then the value of $$\mathrm{V}_{\mathrm{AB}}$$ at this instant will be ____________ $$\mathrm{V}$$.

A certain elastic conducting material is stretched into a circular loop. It is placed with its plane perpendicular to a uniform magnetic field B = 0.8 T. When released the radius of the loop starts shrinking at a constant rate of 2 cms$$^{-1}$$. The induced emf in the loop at an instant when the radius of the loop is 10 cm will be __________ mV.

Three identical resistors with resistance R = 12$$\Omega$$ and two identical inductors with self inductance L = 5 mH are connected to an ideal battery with emf of 12 V as shown in figure. The current through the battery long after the switch has been closed will be _____________ A.

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

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

In a coil of resistance $$8 \,\Omega$$, the magnetic flux due to an external magnetic field varies with time as $$\phi=\frac{2}{3}\left(9-t^{2}\right)$$. The value of total heat produced in the coil, till the flux becomes zero, will be _____________ $$J$$.

Magnetic flux (in weber) in a closed circuit of resistance 20 $$\Omega$$ varies with time t(s) at $$\phi$$ = 8t² $$-$$ 9t + 5. The magnitude of the induced current at t = 0.25 s will be ____________ mA.

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 $$\times$$ 10^$$-$$3 T and the angle of dip is 45$$^\circ$$. The emf induced in the rod is ___________ mV.

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 current in a coil of self inductance 2.0 H is increasing according to I = 2 sin(t²) A. The amount of energy spent during the period when current changes from 0 to 2 A is ____________ J.

A circular coil of 1000 turns each with area 1m² is rotated about its vertical diameter at the rate of one revolution per second in a uniform horizontal magnetic field of 0.07T. The maximum voltage generation will be ___________ V.