$A$ space consists of two uniform magnetic fields,as shown. $A$ conducting circular loop is placed symmetrically at the boundary.

Derive the formula for induced charge and prove that it is independent of the rate of change of magnetic flux.

$A$ uniform magnetic field $\vec{B}$ is perpendicular to the plane of a circular loop of diameter $10 \text{ cm}$ formed from a wire of diameter $2 \text{ mm}$ and resistivity $2 \times 10^{-8} \Omega \text{ m}$. If a current of $11 \text{ A}$ is to be induced in the loop, then the rate at which $\vec{B}$ is to be changed is: (in $\text{ T s}^{-1}$)

$A$ loop of irregular shape of conducting wire (as shown in the figure) is placed in a uniform magnetic field perpendicular to the plane of the paper. If the loop changes into a circular shape,the direction of the induced current will be:

The figure shows a conducting loop placed in a magnetic field. The magnetic flux through the loop changes according to the equation $\phi = 5t - 10t^2$. What is the direction and magnitude of the induced current at $t = 0.25\, s$?

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 $= 10 \ \Omega$]