$A$ conductor $10 \ cm$ long is moved with a speed $1 \ m/s$ perpendicular to a magnetic field of strength $1000 \ A/m$. The e.m.f. induced in the conductor is [Given : $\mu_0 = 4 \pi \times 10^{-7} \ Wb/Am$]

Find the current in the wire for the configuration shown in the figure. Wire $PQ$ has negligible resistance. $\vec{B}$ is the magnetic field coming out of the paper. $\theta$ is a fixed angle made by $PQ$ as it travels smoothly over two conducting parallel wires separated by a distance $d$.

$A$ wire of length $1 \, m$ is moving at a speed of $2 \, ms^{-1}$ perpendicular to its length and a homogeneous magnetic field of $0.5 \, T$. The ends of the wire are joined to a circuit of resistance $6 \, \Omega$. The rate at which work is being done to keep the wire moving at constant speed is:

$A$ square loop of side $20\, {cm}$ and resistance $1\, \Omega$ is moved towards the right with a constant speed ${v}_{0}$. The right arm of the loop is in a uniform magnetic field of $5\, {T}$. The field is perpendicular to the plane of the loop and is directed into it. The loop is connected to a network of resistors,each of value $4\, \Omega$. What should be the value of ${v}_{0}$ so that a steady current of $2\, {mA}$ flows in the loop?

$A$ metallic rod of length '$L$' is rotated with an angular speed of '$\omega$' normal to a uniform magnetic field '$B$' about an axis passing through one end of the rod,as shown in the figure. The induced emf will be:

The magnetic field in a region is given by $\vec B = B_0(1 + \frac{x}{a})\hat k$. $A$ square loop of edge length $d$ is placed with its edges along the $x$ and $y$ axes. The loop is moved with a constant velocity $\vec V = V_0\hat i$. The $emf$ induced in the loop is: