When the switch is closed in the primary circuit,the instantaneous induced current in the secondary circuit is:

$A$ square loop of side $10 \; cm$ and resistance $0.5 \; \Omega$ is placed vertically in the east-west plane. $A$ uniform magnetic field of $0.10 \; T$ is set up across the plane in the north-east direction. The magnetic field is decreased to zero in $0.70 \; s$ at a steady rate. Determine the magnitudes of induced emf and current during this time interval.

The charge which will flow through a galvanometer of resistance $200 \Omega$ connected to a $400 \Omega$ circular coil of $1000$ turns wound on a wooden stick $20 \ mm$ in diameter,if a magnetic field $B=0.012 \ T$ parallel to the axis of the stick is decreased suddenly to zero,is nearly: (in $\mu C$)

$A$ metal ring is held horizontally and a bar magnet is dropped through the ring with its length along the axis of the ring. The acceleration of the falling magnet is

Suppose a long solenoid of $100 \ cm$ length, radius $2 \ cm$ having $500 \ turns/cm$ carries a current $I = 10 \sin(\omega t) \ A$, where $\omega = 1000 \ rad/s$. $A$ circular conducting loop $(B)$ of radius $1 \ cm$ is coaxially placed inside the solenoid. The r.m.s. current through the loop when the coil $B$ is inside the solenoid is $\alpha / \sqrt{2} \ \mu A$. The value of $\alpha$ is . . . . . . . [Resistance of the loop $= 10 \ \Omega$]

$A$ line charge ($\lambda$ per unit length) is in the form of a circular wheel of radius $a$ and moment of inertia $I$,initially at rest. It is free to rotate in a horizontal plane. There is a coaxial magnetic field $B = B_0 \hat{k}$ extending up to a radius $b$ $(b < a)$. If the magnetic field is switched off,the angular velocity $\omega$ of the wheel is given by: