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

The arm $PQ$ of a rectangular conductor is moving from $x=0$ to $x=2b$ outwards and then inwards from $x=2b$ to $x=0$ as shown in the figure. $A$ uniform magnetic field perpendicular to the plane is acting from $x=0$ to $x=b$. Identify the graph showing the variation of different quantities with distance.

$A$ conducting circular loop is rotated about its diameter at a constant angular speed of $100 \ rad/s$ in a magnetic field of $0.5 \ T$ perpendicular to the axis of rotation. When the loop is rotated by $30^{\circ}$ from the horizontal position,the induced $EMF$ is $15.4 \ mV$. The radius of the loop is . . . . . . $mm$. (Take $\pi = 22/7$)

Kamla peddles a stationary bicycle. The pedals of the bicycle are attached to a $100$ turn coil of area $0.10 \; m^2$. The coil rotates at half a revolution per second and it is placed in a uniform magnetic field of $0.01 \; T$ perpendicular to the axis of rotation of the coil. What is the maximum voltage (in $V$) generated in the coil?

To measure a magnetic field between the magnetic poles of a loudspeaker, a small coil having $30$ turns and $2.5 \, cm^2$ area is placed perpendicular to the field and removed immediately. If the total charge flown through the coil is $7.5 \times 10^{-3} \, C$ and the total resistance of the wire and galvanometer is $0.3 \, \Omega$, then the magnitude of the magnetic field is

An infinitely long straight wire carrying current $I$,an open rectangular loop,and a conductor $C$ with a sliding connector are located in the same plane,as shown in the figure. The connector has length $l$ and resistance $R$. It slides to the right with a velocity $v$. The resistance of the conductor and the self-inductance of the loop are negligible. The induced current in the loop,as a function of separation $r$ between the connector and the straight wire,is: