Electromagnetic Induction Questions

$AB$ is a part of an electrical circuit (see figure). The potential difference $V_A-V_B$ at the instant when current $i=2\text{A}$ and is increasing at a rate of $1\text{amp / second}$ is:

A conducting ring of radius $1\text{meter}$ is placed in a uniform magnetic field $B$ of $0.01\text{tesla}$ oscillating with frequency $100\text{Hz}$ with its plane at right angles to $B$. What will be the induced electric field?

A magnet is made to oscillate with a particular frequency, passing through a coil as shown in figure. The time variation of the magnitude of e.m.f. generated across the coil during one cycle is:

A circular disc of radius $0.2\text{meter}$ is placed in a uniform magnetic field of induction $\frac{1}{\pi }{\text{Wb/m}}^2$ in such a way that its axis makes an angle of $60^{\circ }$ with $\vec{B}$. The magnetic flux linked with the disc is:

A long solenoid has $500$ turns. When a current of $2\text{ampere}$ is passed through it, the resulting magnetic flux linked with each turn of the solenoid is $4\times 10^{-3}\text{Wb}$. The self-inductance of the solenoid is:

A rectangular, a square, a circular and an elliptical loop, all in the $(x-y)$ plane, are moving out of a uniform magnetic field with a constant velocity, $\vec{v}=v\hat{i}$. The magnetic field is directed along the negative $z$ axis. The induced emf will not remain constant for:

A conducting circular loop is placed in a uniform magnetic field $0.04\text{T}$ with its plane perpendicular to the magnetic field. The radius of the loop starts shrinking at $2\text{mm/s}$. The induced emf in the loop when the radius is $2\text{cm}$ is:

An electron moves on a straight line path $XY$ as shown. The $abcd$ is a coil adjacent to the path of electron. What will be the direction of current, if any, induced in the coil?

A uniform magnetic field is restricted within a region of radius $r$. The field changes with time at a rate $dB/dt$. Loop 1 of radius $R>r$ encloses the region and loop 2 of radius $R$ is outside the region. The e.m.f. generated is: