Faraday’s Law

A ring made of insulating material is rolling without slipping on a horizontal surface with a velocity of center of mass $V_0.$ A conducting wire of length $2R$ ( $R=$ radius of the ring) is fixed between two points of the circumference. At an instant, the wire is in a vertical position as shown in the figure. A uniform magnetic field, $B$ exists perpendicular to the plane of the ring. The magnitude of emf induced between the ends of the wire is, 

The magnetic field inside a long solenoid of cross-section $15 {\mathrm{cm}}^2$ is $200 \mathrm{T}$. This solenoid crosses a square coil of area $2 {\mathrm{m}}^2$ such that the length of the solenoid is parallel to the axis of coil. The magnetic flux linked through the square coil is $x \mathrm{Wb}$, then what is the value of $10x$?

A conducting rod $pq$ is sliding on two parallel conducting rods with constant velocity in a uniform magnetic field of induction $B=2 \mathrm{Wb} {\mathrm{m}}^{-2}$ as shown in the figure. The rods are connected with a circuit. What should be velocity of rod $pq$ (in $\mathrm{m} {\mathrm{s}}^{-1}$), if current in $2 \mathrm{\Omega }$ resistor is $0.1 \mathrm{A}?$

A ring of mass $4 \mathrm{kg}$ is uniformly charged with a linear charge density $\mathrm{\lambda }=4\mathrm{ }\mathrm{C} {\mathrm{m}}^{-1}$ and kept on a rough horizontal surface with a friction coefficient of $\mathrm{\mu }=\frac{\mathrm{\pi }}{4}$. A time-varying magnetic field $\mathrm{B}={\mathrm{B}}_0{\mathrm{t}}^2$ is applied in a circular region of radius $\mathrm{a}$ $\left(\mathrm{a}<\mathrm{r}\right)$ perpendicular to the plane of the ring as shown in the figure. Find out the time (in seconds) when the ring just starts to rotate on the surface. ( Take $\mathrm{a}=5 \mathrm{cm}$, $\mathrm{g}=10\mathrm{ }\mathrm{m} {\mathrm{s}}^{-2}$ and ${\mathrm{B}}_0=125 \mathrm{T} {\mathrm{s}}^{-2}$)

A solenoid $1.0 \mathrm{m}$ long and $0.04 \mathrm{m}$ in diameter has $700$ turns. Another solenoid of $50$ turns is tightly wound over the first solenoid. Then, the emf induced in the second solenoid when the current in the first solenoid changes from $0$ to $5 \mathrm{A}$ in $0.01 \mathrm{s}$ (Take, ${\pi }^2=10$) is $n\times {10}^{-2} \mathrm{V}$. Find $n⟶$(ignore edge effects).

A metallic loop is placed in a uniform magnetic field $B$ with the plane of the loop perpendicular to $B.$ Under which condition (s) given an emf will be induced in the loop? "If the loop is .....

A uniform but time varying magnetic field exists in cylindrical region and directed into the paper. If field decreases with time and a positive charge is placed at any point inside the region, then it moves 

The magnetic flux through each turn of a $100$ turn coil is $\left(t^3-2t\right)\times {10}^{-3} \mathrm{Wb}$, where $t$ is in second. The induced emf at $t=2 \mathrm{s}$ is

To convert mechanical energy into electrical energy, one can use which of the following?

A rod AB moves with a uniform velocity $v$ in a uniform magnetic field as shown in the figure

A conducting rod is moved with a constant velocity $v$ in a magnetic field. A potential difference appears across the two ends

A current carrying infinitely long wire is kept along the diameter of a circular wire loop, without touching it. The correct statement (s) is (are):

A thin non-conducting ring of mass $m$ and radius $a$ carrying a charge $q$ can rotate freely about its own axis which is vertical. At the initial moment the ring was at rest in horizontal position and no magnetic field was present. At instant $t=0$, a uniform magnetic field is switched on which is vertically downward and increases with time according to the law $B=B_{0}t$. Neglecting magnetism induced due to rotational motion of ring.The magnitude of the electric field on the surface of the ring is:

A triangular loop, as shown in the figure, is being pulled out at $t=0$ from a uniform magnetic field with a constant velocity $v.$ The total resistance of the loop is constant and is equal to $R$. Then, the variation of power produced in the loop with time will be,

A plane rectangular loop is placed in a magnetic field. The emf induced in the loop due to this field is ${\epsilon }_i$ whose maximum value is ${\epsilon }_{im}$. The loop was pulled out of the magnetic field at a variable velocity. Assume that $\overrightarrow{B}$ is uniform and constant. ${\epsilon }_i$ is plotted against time $t$ as shown in the graph. Which of the following is/are correct?

The magnetic field within a cylindrical region, whose cross-section is as indicated, starts increasing at a constant rate of $\alpha \mathrm{T} {\mathrm{s}}^{-1}$. The graph showing the variation of induced field with distance $r$ from the axis of cylinder is:

A square coil $ABCD$ is lying in $xy$ plane with its centre at origin. A long straight wire passing through origin carries a current $i=2t$ in the negative $z$ direction. The induced current in the coil is,

The graph shows the variation in magnetic flux $\varphi \left(t\right)$ with time through a coil. Which of the statements given below is not correct?

A conductor $ABOCD$ moves along its bisector with a velocity of $1 \mathrm{m} {\mathrm{s}}^{-1}$ through a perpendicular magnetic field of $1 \mathrm{Wb} {\mathrm{m}}^{-2}$, as shown in the figure. If all the four sides are of $1 \mathrm{m}$ length each, then the induced emf between points $A$ and $D$ is,

At a place, the value of horizontal component of the earth's magnetic field $H$ is $3\times {10}^{-5}$ $\mathrm{weber} {\mathrm{m}}^{-2}$. A metallic rod $AB$ of length $2 \mathrm{m}$ placed in east-west direction, having the end A towards east, falls vertically downward with a constant velocity of $50 \mathrm{m} {\mathrm{s}}^{-1}$. Which end of the rod becomes positively charged and what is the value of induced potential difference between the two ends?