Induced EMF and Current

A square shaped coil of area $70 {\mathrm{cm}}^2$ having$600$ turns rotates in a magnetic field of $0.4 \mathrm{Wb} {\mathrm{m}}^{-2}$, about an axis which is parallel to one of the side of the coil and perpendicular to the direction of field. If the coil completes$500$revolutions in a minute, the instantaneous emf when the plane of the coil is inclined at $60°$ with the field, will be______ $\mathrm{V}$. (Take $\pi =\frac{22}{7}$)

A metal disc is made to spin at $20$ revolutions per second about an axis passing through its centre and normal to its plane. The disc has a radius of$30 \mathrm{cm}$ and spins in a uniform magnetic field of $0.20 \mathrm{T}$, which is parallel to the axis of rotation. Calculate
(a) The area swept out per second by the radius of the disc,
(b) The flux cut per second by a radius of the disc,
(c) The induced emf in the disc.

A metal rod of length  $L$metre rotates about one end in a vertical plane at right angles to the magnetic meridian. Frequency of revolution is$f \mathrm{Hz}$. If the horizontal component of earth's magnetic field is$H$Tesla, then find an expression of induced emf between the ends of the rod. 

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 $t=2 \mathrm{s}$ to $t=4 \mathrm{s}$, is _____ $mV$.

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 $12 \mathrm{\Omega }$. 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 $1 \mathrm{mm} {\mathrm{s}}^{-1}$. The magnitude of induced emf in the loop at an instant when the radius of the loop is $2 \mathrm{cm}$ will be _______ $\mathrm{\mu V}$.

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 ___________

$($ Take, $\left.\pi =\frac{22}{7}\right)$

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 circular ring is placed in magnetic field of $0.4 \mathrm{T}$. Suddenly, its radius starts shrinking at the rate of $1 \mathrm{mm} {\mathrm{s}}^{-1}$. Find the induced emf in the ring at $r = 2 \mathrm{cm}$.

Variation of magnetic field through a coil of area $4 {\mathrm{m}}^2$ is shown in figure. What is the EMF induced in the coil (in $\mathrm{mV}$)?

A circular coil of $100$ turns has radius $4 \mathrm{cm}$. It is placed with its plane perpendicular to a magnetic field of $3 \mathrm{T}$. If the magnetic field reduces to $1 \mathrm{T}$ in $0.2 \mathrm{s}$, Calculate the e.m.f. induced in the coil.

 If a conductor is moved in a direction parallel to the magnetic field, no induced current will be developed in the conductor?
 

The magnetic flux through a circuit carrying a current of $2.0 \mathrm{A}$ is $0.8$weber. If the current reduces to $1.5 \mathrm{A}$in$0.1 \mathrm{s}$, the induced emf be.

A square loop of side $10 \mathrm{cm}$ with its side parallel to X and Y axes is moved with a velocity of$8 \mathrm{cm} {\mathrm{s}}^{-1}$ in the positive X - direction containing a magnetic field in positive Z - direction. The field is non-uniform and has a gradient of $8 \mathrm{cm} {\mathrm{s}}^{-1}$ along the negative X - direction (i.e. it increases by ${10}^{-3} \mathrm{T} {\mathrm{cm}}^{-1}$as one moves in the negative X- direction). Calculate the emf induced.

Through a long solenoid of diameter $4.1 \mathrm{cm}$, having $100$ turns per $\mathrm{cm}$, a current $I=1 \mathrm{A}$ is flowing. At its centre, a $60$ turns closely packed coil of diameter $3.1 \mathrm{cm}$ is placed such that the coil is co-axial with the long solenoid. The current in the solenoid is reduced to zero at a steady rate in $10 \mathrm{ms}$. What is the magnitude of emf induced in the coil while the current in the solenoid is changing?

Consider an LC circuit, with inductance $L=0.1 \mathrm{H}$ and capacitance $C={10}^{-3} \mathrm{F}$, kept on a plane. The area of the circuit is $1 {\mathrm{m}}^2$. 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 magnetic field strength starts increasing linearly as $B=B_0+\beta t$ with $\beta = 0.04 \mathrm{T} {\mathrm{s}}^{-1}$. The maximum magnitude of the current in the circuit is $\mathrm{\_\_\_mA}$.

A long solenoid contains $1000$ turns/cm and an alternating current of peak value $1 \mathrm{A}$ is flowing in it. A search coil of area of cross-section $1\times {10}^{-4} {\mathrm{m}}^2$ and having $50$ turns is placed inside the solenoid with its plane perpendicular to the axis of the solenoid. A peak voltage of $2{\pi }^2\times {10}^{-2} \mathrm{V}$ is produced in the search coil. The frequency of current in the solenoid will be

A wire frame in the form of a sector of radius $l$ and resistance $R$ is free to rotate about an axis passing through $O$ and perpendicular to the plane of paper. A constant and uniform magnetic field of magnitude $B$ exits in the space above the line $PQ$ as shown in figure. Direction of the magnetic field in region $\mathrm{I}$ and $\mathrm{II}$ is outward and inward to the plane of paper respectively as shown in the figure. The sector rotates with constant angular velocity $\omega$. Find the average power produced in the wire frame.

The magnetic flux through a coil perpendicular to the plane is varying according to the relation $\varphi =5t^3+6t^2+5t+6 \mathrm{Wb}$. Calculate the induced current through the coil at $t=2 \mathrm{s}$, if the resistance of the coil is $\mathrm{R}=5 \mathrm{\Omega }$.