The magnetic flux through a stationary loop with resistance $R$ varies during interval of time $T$ as $\varphi =\mathrm{at}\left(T-t\right)$. The heat generated during this time neglecting the inductance of loop will be: -

The figure shows an isosceles triangle wire frame with apex angle equal to $\frac{\pi }{2}$. The frame starts entering into the region of uniform magnetic field $B$ with constant velocity $v$ at $t=0$. The longest side of the frame is perpendicular to the direction of velocity. If $i$ is the instantaneous current through the frame then choose the alternative showing the correct variation of $i$ with time.

Two parallel long straight conductors lie on a smooth surface. Two other parallel conductors rest on them at right angles so as to form a square of side a initially. $A$ uniform magnetic field $B$ exists at right angles to the plane containing the conductors. They all start moving out with a constant velocity $v$. If $r$ is the resistance per unit length of the wire the current in the circuit will be

A conducting rod $PQ$ of length $5 \mathrm{m}$ oriented as shown in figure is moving with velocity $2( \mathrm{m} {\mathrm{s}}^{-1})$ without any rotation in a uniform magnetic field $\overrightarrow{B}=3\hat{j}+4\hat{k}$ Tesla. Magnitude of induced $EMF$ in the rod is:

When a '$\mathrm{J}$' shaped conducting rod is rotating in its own plane with constant angular velocity $\omega$, about one of its end $P$, in a uniform magnetic field $\overrightarrow{B}$ directed normally into the plane of paper) then magnitude of emf induced across it will be

A metal disc rotates freely, between the poles of a magnet in the direction indicated. Brushes $P$ and $Q$ make contact with the edge of the disc and the metal axle. What current, if any, flows through $R$ ?

In the circuit shown, the cell is ideal. The coil has an inductance of $4 H$ and zero resistance. $F$ is a fuse of zero resistance and will blow when the current through it reaches $5 A$. The switch is closed at $t=0$ The fuse will blow: