As shown in the figure,a metal rod makes contact and completes the circuit. The circuit is perpendicular to the magnetic field with $B = 0.15 \, T$. If the resistance is $3 \, \Omega$,the force needed to move the rod as indicated with a constant speed of $2 \, m/s$ is:

If a wheel with $24$ metallic spokes each $40 \ cm$ long is rotated with a speed of $180 \ rev/min$ in a plane normal to the horizontal component of earth's magnetic field, the emf induced between the axle and the rim of the wheel is $E$. If the number of spokes is made $12$ and the wheel is rotated with a speed of $90 \ rev/min$ in the same field, the induced emf is

Two straight conducting plates form an angle $\theta$ where their ends are joined. $A$ conducting bar in contact with the plates and forming an isosceles triangle with them starts at the vertex at time $t=0$ and moves with constant velocity $\vec{v}$ to the right as shown in the figure. $A$ magnetic field $\vec{B}$ points out of the page. The magnitude of the emf induced at $t=1 \text{ s}$ will be

$A$ rod of mass $m$ and resistance $R$ slides smoothly over two parallel perfectly conducting wires kept sloping at an angle $\theta$ with respect to the horizontal as shown in the figure. The circuit is closed through a perfect conductor at the top. There is a constant magnetic field $\vec{B}$ along the vertical direction. If the rod is initially at rest,find the velocity of the rod as a function of time.

The figure shows an isosceles triangle wire frame with an apex angle equal to $\pi / 2$. The frame starts entering into the region of a uniform magnetic field $B$ with a 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.

$A$ conducting rod of length $2l$ is rotating with constant angular speed $\omega$ about its perpendicular bisector. $A$ uniform magnetic field $\vec{B}$ exists parallel to the axis of rotation. The $e.m.f.$ induced between two ends of the rod is