An infinitely long wire carries current $i_0$ along $+z$ axis. Find flux through the right angled isosceles triangular region coplanar with the wire as shown in figure.

The loop moves towards a region of magnetic field. Draw graph of $i(+$ ve direction is marked in figure $)$ and time. Speed of coil is constant and equal to $v .$.

The loop shown in figure is rotating with angular velocity $\omega$ around a perpendicular axis passing through $O$. Which of the following graph correctly represent emf developed in the loop as function of $\theta$ ? ( $\theta$ is shown in diagram) (Consider anti-clockwise current due to $+ ve$ emf)

A rod is moving on rails as shown in figure. Outside magnetic field is given by $B_0$. Resistance of system is $R$ and length is $l .$

(a) Find direction of induced current.
(b) Find emf and current.
(c) Find magnetic force on the rod.

The wire is shaped like a parabola $y^2=4ax$, and the magnetic field is uniform and out of the plane of the paper perpendicularly. At the instant the rod crosses the point $(a, 0)$. Induced emf in the rod is

Magnetic field in a cylindrical region is given by $B=\alpha t$. Find emf across rod $AB$ as shown in figure.

A charge $q$, mass $m$ is lying in a cylindrical region of magnetic field at point $P$. If magnetic field in the region is given by $B_0$ and $P$ is at distance $R$ from centre of region, find speed of charge if the magnetic field is suddenly switched off

Network shown in the diagram is part of an electrical circuit. The current is $2 A$ and is decreasing at the rate of $2 \frac{A}{s}$ then $V_P-V_Q$ equals