In the given branch $AB$ of a circuit,a current $I = (10t + 5) \, A$ is flowing,where $t$ is time in seconds. At $t = 0$,the potential difference between points $A$ and $B$ $(V_A - V_B)$ is.....$V$.

$A$ square loop of area $25 \, cm^2$ has a resistance of $10 \, \Omega$. The loop is placed in a uniform magnetic field of magnitude $40 \, T$. The plane of the loop is perpendicular to the magnetic field. The work done in pulling the loop out of the magnetic field slowly and uniformly in $1 \, s$ will be:

Derive the equation for the induced $emf$ in a rod of length $l$ sliding with velocity $v$ on a $U$-shaped frame placed perpendicular to a uniform magnetic field $B$.

$A$ rod of length $l$ is rotating in the plane of the paper with an angular speed $\omega$ about one of its ends,which is at a distance $a$ from an infinitely long conducting wire carrying current $i$ inwards the plane of the paper. Find the induced $emf$ in the rod at the instant as shown in the figure.

$A$ $800$ turn coil of effective area $0.05\; m^{2}$ is kept perpendicular to a magnetic field $5 \times 10^{-5}\; T$. When the plane of the coil is rotated by $90^{\circ}$ around any of its coplanar axes in $0.1\; s$,the $emf$ induced in the coil will be.....$V$

The loops have lengths $L$ or $2L$. All loops enter a magnetic field $\vec{B}$ with the same velocity $v$. Which of the following is correct?