The radius of the circular conducting loop shown in the figure is $R.$ The magnetic field is decreasing at a constant rate $\alpha.$ The resistance per unit length of the loop is $r.$ Find the current in the wire $AB,$ where $AB$ is one of the diameters.

$A$ magnetic field in a certain region is given by $\vec B = B_0 \cos(\omega t) \hat k$. $A$ coil of radius $a$ with resistance $R$ is placed in the $xy$-plane with its centre at the origin in the magnetic field (see figure). Find the magnitude and the direction of the current at $(a, 0, 0)$ at $t = \frac{\pi}{2\omega}$,$t = \frac{\pi}{\omega}$,and $t = \frac{3\pi}{2\omega}$.

Consider an infinitely long wire carrying a current $I(t)$,with $\frac{dI}{dt} = \lambda = \text{constant}$. Find the current produced in the rectangular loop of wire $ABCD$ if its resistance is $R$ as shown in the figure.

$A$ solenoid of radius $R$ and length $L$ has a current $I = I_0 \sin \omega t$. The value of the induced electric field at a distance $r$ inside the solenoid is:

In the diagram shown,a time-varying non-uniform magnetic field passes through a circular region of radius $R$. The magnetic field is directed outwards and it is a function of radial distance $r$ and time $t$ according to the relation $B = B_0rt$. What is the induced electric field strength at a radial distance $R/2$ from the center?

$A$ metallic ring of radius $a$ and resistance $R$ is held fixed with its axis along a spatially uniform magnetic field whose magnitude is $B = B_0 \sin \omega t$. Gravity is neglected. Then,