Magnetic Flux & Faraday's Law

A circular disc of radius 20 cm is placed in uniform magnetic field of induction $\frac{7}{22}$ Wb/m$^{2}$ in such a way that its axis makes an angle of $60^\circ$ with $\vec{B}$. The magnetic flux linked with the disc is $(\cos 60^\circ = 0.5)$

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

Whenever a magnet is moved either towards or away from a conducting coil, magnetic flux linked with the coil changes. This change is dependent on

(a) the strength of the magnetic field.

(b) the area of cross-section of the coil.

(c) the resistance of the coil.

(d) the number of turns in the coil.

A coil of effective area $3$ m$^{2}$ is placed at right angles to a magnetic field of induction $0.05$ Wb/m$^{2}$. If the field is decreased to $20\%$ of its original value in $10$ second, the e.m.f. induced in the coil will be

A conducting loop of radius $10/[\pi]^{1/2}$ cm is placed perpendicular to a uniform magnetic field $0.5$ 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

Magnetic flux linked with the coil in weber is given by the equation $\Phi = 5t^{2} + 6t + 11$. The e.m.f. induced in the coil in the $5$th second will be

A coil of 'n' turns and resistance $R\,\Omega$ is connected in series with a resistance $R/4$. The combination is moved for time 't' second through flux $\Phi_1$ to $\Phi_2$. The induced current in the circuit is

A coil having 'n' turns and resistance 'R' is connected with a galvanometer of resistance '2R'. This combination is moved in time 't' from flux $\phi_1$ to $\phi_2$ Wb. The induced current in the circuit is

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

An induced current of $2$A flows through a coil. The resistance of the coil is $10\ \Omega$. What is the change in magnetic flux associated with a coil in $1$ ms?

A square of side L metre lies in the XY plane in a region, where the magnetic field is $\vec{B} = B_0\,(2\hat{i} + 3\hat{j} + 4\hat{k})$, where $B_0$ constant. The magnitude of flux passing through the square is

The coil of area $0.1$ m$^{2}$ has $1000$ turns. It is placed in a magnetic field of strength $5 \times 10^{-4}$ T. The average e.m.f. induced in the coil, if rotated through $180^\circ$ in $0.1$ s is ($\cos 0^\circ = 1, \cos 180^\circ = -1$)

A varying magnetic flux linking a coil is $\Phi = xt^{2}$. If at time $t = 3$ s, the e.m.f. induced is $9$V then the magnitude of $x$ is (in Wb$/\text{s}^{2}$)

A square loop of side 2 cm is placed in a time varying magnetic field with magnitude as $B = 0.4\sin(300t)$ Tesla. The normal to the plane of loop makes an angle of $60^\circ$ with the field. The maximum induced emf produced in the loop is ______ mV.

A circular loop of radius 7 cm is placed in uniform magnetic field of 0.2 T directed perpendicular to plane of loop. The loop is converted into a square loop in 0.5 s. The EMF induced in the loop is ______ mV.

A circular ring of diameter $20$ cm has a resistance of $0.01\ \Omega$. The charge that will flow through the ring, if it is turned from a position perpendicular to a uniform magnetic field of $2$T to a position parallel to the field is (in coulomb) ($\because \cos 0^\circ = 1,\ \cos 90^\circ = 0$)

A closed coil consists of $500$ turns on a rectangular frame of area $4.0$ cm$^{2}$ and has a resistance of $50\ \Omega$. The coil is kept with its plane perpendicular to a uniform magnetic field of $0.2$ T. The amount of charge flowing through the coil if it is turned through $180^\circ$ will be $1.6 \times 10^{-x}$ C. The Value of $x$ is

A rectangular wire loop of resistance $1.5\ \Omega$ placed in a region of uniform magnetic field of magnitude $0.3$ T directed normal to the loop. If the area of the loop decreases at a rate of $0.05$ m${}^{2}/\text{s}$ in this magnetic field, the heat produced in it is $x \times 10^{-6}$ W. The value of $x$ is

A conducting loop of finite resistance lies on the $x-y$ plane. There is a constant magnetic field in the $z$ direction. The area of the loop varies with time $t$, as $A = A_0(1+\sin t)$ in appropriate units. The figure that correctly indicates the qualitative behaviour of the power $P$ dissipated in the loop as a function of time is:

A conducting circular loop of area $1.0\text{ m}^{2}$ is placed perpendicular to a magnetic field which varies as $B = \sin(100t)$ Tesla. If the resistance of the loop is $100\ \Omega$, then the average thermal energy dissipated in the loop in one period is ______ J.

A circular loop of radius 20 cm and resistance $2\ \Omega$ is placed in a time varying magnetic field $\vec{B} = \left(2t^{2}+2t+3\right)T$. At $t = 0$, for the plane of the loop being perpendicular to the magnetic field and, the induced current in the loop at $t = 3\text{ s}$ is $\frac{\alpha}{50}\text{ A}$. The value of $\alpha$ is ______. (Take $\pi = 22/7$)

When a coil is placed in a time dependent magnetic field the power dissipated in it is $P$. The number of turns, area of the coil and radius of the coil wire are $N,\ A$ and $r$ respectively. For a second coil number of turns, area of the coil and radius of the coil wire are $2N,\ 2A$ and $3r$ respectively. When the first coil is replaced with second coil the power dissipated in it is $\sqrt{2}\,\alpha P$. The value of $\alpha$ is ______.

A coil of effective area $3\text{ m}^{2}$ is placed at right angles to a magnetic field of induction $0.05\text{ Wb/m}^{2}$ If the field is decreased to $20\%$ of its original value in 10 second, the e.m.f. induced in the coil will be

A magnetic field $4 \times 10^{-2}\text{ T}$ acts at right angles to a coil of area $100\text{ cm}^{2}$ 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

A coil having ' $N$ ' turns and resistance ' $R$ ' $\Omega$ is connected to a galvanometer of resistance ' 6 R ' $\Omega$. The magnetic flux linked with this coil changes from $\phi_1$ weber to $\phi_2$ weber in time ' t ' second. The induced current in the circuit is

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

A coil of n turns and resistance $R\Omega$ is connected in series with resistance $R/4$. The combination is moved for time $t$ second through magnetic flux $\phi_1$ to $\phi_2$. The induced current in the circuit is

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

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

The magnetic flux through a coil is $4 \times 10^{-4}\text{ Wb}$ 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 coil of ' $n$ ' turns and area ' $A$ ' is suddenly removed from a magnetic field, a charge ' $q$ ' flows through the coil. If resistance of the coil is ' $R$ ' then the magnetic flux density is (in $\text{Wb/m}^{2}$)

A magnetic field of $2 \times 10^{-2}\text{ T}$ acts at right angles to a coil of area $100\text{ cm}^{2}$ 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 coil of resistance $250\,\Omega$ is placed in a magnetic field. If the magnetic flux $(\phi)$ linked with the coil varies with time $t(\text{s})$ as $\phi = 50t^{2} + 7$. The current in the coil at $t = 4\text{ s}$ is

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

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

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

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

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

The net magnetic flux through any closed surface is:

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:

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

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

A coil having effective area '$A$' is held with its plane normal to a magnitude field of induction '$B$'. 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

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

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

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

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.

An insulated copper wire of 100 turns is wrapped around a wooden cylindrical core of the cross- sectional area $24\text{ cm}^{2}$. 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 $1.5\text{ T}$ in one direction to $1.5\text{ T}$ in the opposite direction, the charge flowing through a point in the circuit during the change of magnetic field will be ___________ $\text{mC}$.

A square loop of side 1 m and resistance 1 $\Omega$ is placed in a magnetic field of 0.5 T. If the plane of loop is perpendicular to the direction of magnetic field, the magnetic flux through the loop is

The magnetic flux linked to a circular coil of radius R is

$\phi = 2t^{3} + 4t^{2} + 2t + 5$ Wb

The magnitude of induced emf in the coil at t = 5 s is

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

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.

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

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 $1\text{ m}$, the induced emf in the loop, at time, $t = 2\text{ s}$ is $n\pi\text{ V}$. The value of $n$ 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.)

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 _____________ $\text{J}$.

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

At what rate a single conductor should cut the magnetic flux so that current of $1.5\text{ mA}$ 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 $\phi = 5t^{2} - 6t + 9$. The magnitude of induced current at $t = 0.2$ second is

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

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

$[\cos 0^\circ = \sin 90^\circ = 1$ and $\sin 0^\circ = \cos 90^\circ = 0]$

In the given figure the magnetic flux through the loop increases according to the relation $\phi$B(t) = 10t2 + 20t, where $\phi$B is in milliwebers and t is in seconds.

The magnitude of current through R = 2$\Omega$ resistor at t = 5 s is ___________ mA.

A circular conducting coil of radius 1 m is 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 time as

$B = \frac{4}{\pi} \times 10^{-3}\,T\left(1-\frac{t}{100}\right)$

The energy dissipated by the coil before the magnetic field is switched off completely is E = ___________ mJ.

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 loop is:

The magnetic flux linked with a coil (in Wb) is given by the equation

$\phi = 5t^{2} + 3t + 16$

The magnitude of induced emf in the coil at the fourth second will be

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

Consider a circular coil of wire carrying constant current I, forming a magnetic dipole. The magnetic flux through an infinite plane that contains the circular coil and excluding the circular coil area is given by $\phi$i. The magnetic flux through the area of the circular coil area is given by $\phi$0. Which of the following option is correct?

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 Ts–1. The induced current in the loop is close to (Resistivity of the metal wire is 1.23 $\times$ 10–8 $\Omega$m)

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 is $\vec{B} = \left(3\hat{i}+4\hat{k}\right)T$. The quantity of flux through the loop ABCDEFA (in Wb) is _______.

A 800 turn coil of effective area 0.05 m2 is kept perpendicular to a magnetic field 5 × 10–5 T. When the plane of the coil is rotated by 90° around any of its coplanar axis in 0.1 s, the emf induced in the coil will be:

A conducting circular loop made of a thin wire, has area 3.5 $\times$ 10$-$3 m2 and resistance 10 $\Omega$. It is placed perpendicular to a time dependent magnetic field B(t) = (0.4T)sin(50$\pi$t). The field is uniform in space. Then the net charge flowing through the loop during t = 0 s and t = 10 ms is close to:

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:

A long solenoid of diameter 0.1 m has 2 $\times$ 104 turns per meter. At the centre of the solenoid, a coil of 100 turns and radius 0.01 m is placed with its axis coinciding with the solenoid axis. The current in the solenoid reduces at a constant rate to 0 A from 4 A in 0.05 s. If the resistance of the coil is 10 $\pi$2 $\Omega$, the total charge flowing through the coil during this time is

A conducting metal circular-wire-loop of radius r is placed perpendicular to a magnetic field which varies with time as

B = B0e$\frac{-t}{\tau}$, where B0 and $\tau$ are constants, at time t = 0. If the resistance of the loop is R then the heat generated in the loop after a long time (t $\to \infty$) is:

A coil of circular cross-section having 1000 turns and 4 cm2 face area is placed with its axis parallel to a magnetic field which decreases by 10$-$2 Wb m${}^{-2}$ in 0.01 s. The e.m.f. induced in the coil is:

A coil of resistance 400 $\Omega$ is placed in a magnetic field. If the magnetic flux $\phi$ (Wb) linked with the coil varies with time t (sec) as $\phi = 50t^{2} + 4$.

The current in the coil at t = 2 sec is

In a coil of resistance 10 $\Omega$, the induced current developed by changing magnetic flux through it, is shown in figure as a function of time. The magnitude of change in flux through the coil in weber is

A conducting circular loop is placed in a uniform magnetic field, B = 0.025 T with its plane perpendicular to the loop. The radius of the loop is made to shrink at a constant rate of 1 mm s${}^{-1}$. The induced emf when the radius is 2 cm, is

A conducting circular loop is placed in a uniform magnetic field 0.04 T with its plane perpendicular to the magnetic field. The radius of the loop starts shrinking at 2 mm/s. The induced emf in the loop when the radius is 2 cm is

A circular disc of radius 0.2 meter is placed in a uniform magnetic field of induction $\frac{1}{\pi}\left(\frac{\text{Wb}}{\text{m}^{2}}\right)$ in such a way that its axis makes an angle of 60° with $\vec{B}.$ The magnetic flux linked with the disc is

The flux linked with a coil at any instant $\text{'}t\text{'}$ is given by

$\phi = 10t^{2} - 50t + 250$

The induced $emf$ at $t = 3\text{ s}$ is

A coil having $n$ turns and resistance $R\Omega$ is connected with a galvanometer of resistance $4R\Omega.$ This combination is moved in time $t$ seconds from a magnetic field $W_1$ weber to $W_2$ weber. The induced current in the circuit is

The magnetic flux through a circuit of resistance R changes by an amount $\Delta\phi$ in a time $\Delta$t. Then the total quantity of electric charge Q that passes any point in the circuit during the time $\Delta$t is represented by

A rectangular coil of 20 turns and area of cross-section 25 sq. cm has a resistance of $100\ \Omega$. If a magnetic field which is perpendicular to the plane of coil changes at a rate of 1000 tesla per second, the current in the coil is

The total charge, induced in a conducting loop when it is moved in magnetic field depend on

A magnetic field of $2 \times 10^{-2}\text{ T}$ acts at right angles to a coil of area $100\text{ cm}^{2}$, with 50 turns. The average e.m.f. induced in the coil is 0.1 V, when it is removed from the field in $t$ sec. The value of $t$ is