A long U-shaped wire of width $l$ placed in a perpendicular uniform and constant magnetic field $\mathrm{B}$ (figure). A wire of length $l$ is slid on the U-shaped wire with a constant velocity $\mathrm{v}$ towards right. The resistance of all the wires is $\mathrm{r}$ per unit length. At $\mathrm{t} = 0$, the sliding wire is close to the left edge of the fixed U-shaped wire. Draw an equivalent circuit diagram at time $\mathrm{t}$, showing the induced emf as a battery. Calculate the current in the circuit.

 

A long U-shaped wire of width $l$ placed in a perpendicular uniform and constant magnetic field $\mathrm{B}$ (figure). A wire of length $l$ is slid on the U-shaped wire with a constant velocity $\mathrm{v}$ towards right. The resistance of all the wires is $\mathrm{r}$ per unit length. At $\mathrm{t} = 0$, the sliding wire is close to the left edge of the fixed U-shaped wire. Draw an equivalent circuit diagram at time $\mathrm{t}$, showing the induced emf as a battery. Calculate the current in the circuit.

A wire of mass $\mathrm{m}$ and length $l$ can slide freely on a pair of fixed, smooth, vertical rails (figure). A magnetic field $\mathrm{B}$ exists in the region in the direction perpendicular to the plane of the rails. The rails are connected at the top end by an initially uncharged capacitor of capacitance $\mathrm{C}$. Find the velocity of the wire at any time $\left(\mathrm{t}\right)$ after released. Neglecting any electric resistance. (initial velocity of wire is zero)

Figure shows a fixed square frame of wire having a total resistance $r$ placed coplanarly with a long, straight wire. The wire carries a current $\mathrm{i}$ given by $i=i_0 cos\left(\frac{2\pi t}{T}\right)$. Find (a) the flux of the magnetic field through the square frame, (b) the emf induced in the frame and (c) the heat developed in the frame in the time interval $0$ to $10T$.

A straight wire with a resistance of $\mathrm{r}$ per unit length is bent to form an angle $2\mathrm{\alpha }$. A rod of the same wire perpendicular to the angle bisector (of $2\mathrm{\alpha }$) forms a closed triangular loop. This loop is placed in a uniform magnetic field of induction $\mathrm{B}$. Calculate the current in the wires when the rod moves at a constant speed $\mathrm{V}$.

A metal rod of length $15 \times {10}^{–2} \mathrm{m}$ rotates about an axis passing through one end with a uniform angular velocity of $60 \mathrm{rad} {\mathrm{s}}^{–1}.$ A uniform magnetic field of $0.1$ Tesla exists in the direction of the axis of rotation. Calculate the EMF induced between the ends of the rod.

In the figure there are two identical conducting rods each of length $‘\mathrm{a}’$ rotating with angular speed $\mathrm{\omega }$ in the directions shown. One end of each rod touches a conducting ring. Magnetic field $\mathrm{B}$ exists perpendicular to the plane of the rings. The rods, the conducting rings and the lead wires are resistanceless. Find the magnitude and direction of current in the resistance $\mathrm{R}$.