A current carrying loop of radius $R$ and mass$\text{'}m\text{'}$ is placed inside a uniform magnetic field an shown

In a thin rectangular metallic strip a constant current I flows along the positive x - direction, as shown in the figure. The length, width and thickness of the strip are l, w and d, respectively. A uniform magnetic field $\overrightarrow{\text{B}}$ is applied on the strip along positive y - direction. Due to this the charge carries experience a net deflection along the z-direction. This results in accumulation of charge carriers on the surface PQRS and appearance of equal opposite charges on the face opposite to PQRS. A potential difference along the z - direction is thus developed. Charge accumulation continues until the magnetic force is balanced by the electric force. The current is assumed to be uniformly distributed on the cross section of the strip and carried by electrons.

Consider two different metallic strips (1 and 2) of the same material. Their lengths are the same, widths are $w_1$ and $w_2$ and thicknesses are $d_1$ and $d_2$ , respectively. Two points $K$ and $M$ are symmetrically located on the opposite faces parallel to the $x$ - $y$ plane (see figure). $V_1$ and $V_2$ are the potential differences between $K$ and $M$ in strips 1 and 2 respectively. Then, for a given current $I$ flowing through them in a given magnetic field strength $B$ , the correct statement(s) is (are)

Let $F_A$ and $F_B$ be the magnitude of the force between the two wires in setup $A$ and setup $B$, respectively.

The magnitude and direction of a force vector acting on a unit length of thin wire carrying a current $I$ at point $O$, if the wire has a semicircular shape of radius $R$ as shown in the figure.

A circular coil of radius $R$ and $N$ turns has negligible resistance. As shown in the schematic figure, its two ends are connected to two wires and it is hanging by those wires with its plane being vertical. The wires are connected to a capacitor with charge $Q$ through a switch. The coil is in a horizontal uniform magnetic field $B_o$ parallel to the plane of the coil. When the switch is closed, the capacitor gets discharged through the coil in a very short time. By the time the capacitor is discharged fully, magnitude of the angular momentum gained by the coil will be (assume that the discharge time is so short that the coil has hardly rotated during this time)

A copper rod of mass $m$ slides under gravity on two smooth parallel rails $l$ distance apart and set an angle $\theta$ to the horizontal. At the bottom, the rails are joined by a resistance $R$ in figure. There is a uniform magnetic field $B$ perpendicular to the plane of the rails. The terminal velocity of rod is

An elliptical loop having resistance $R$, of semi major axis $a$ , and semi minor axis $b$  is placed in a magnetic field as shown in the figure. If the loop is rotated about the $x$-axis with angular frequency $\omega$, the average power loss in the loop due to Joule heating is :

In a thin rectangular metallic strip a constant current I flows along the positive x - direction, as shown in the figure. The length, width and thickness of the strip are l, w and d, respectively. A uniform magnetic field $\overrightarrow{\text{B}}$ is applied on the strip along positive y - direction. Due to this the charge carries experience a net deflection along the z-direction. This results in accumulation of charge carriers on the surface PQRS and appearance of equal opposite charges on the face opposite to PQRS. A potential difference along the z - direction is thus developed. Charge accumulation continues until the magnetic force is balanced by the electric force. The current is assumed to be uniformly distributed on the cross section of the strip and carried by electrons.

Consider two different metallic strips (1 and 2) of same dimensions (length $l$ , width $w$ and thickness $d$ ) with carrier densities $n_1$ and $n_2$ , respectively. Strip 1 is placed in magnetic field $B_1$ and strip 2 is placed in magnetic field $B_2$ , both along positive $y$ -directions. Then $V_1$ and $V_2$ are the potential differences developed between $K$ and $M$ in strips 1 and 2 respectively. Assuming that the current $I$ is the same for both strips, the correct option(s) is (are)

A wire carrying current $I$ is tied between points $P$ and $Q$ and is in the shape of a circular arc of radius $R$ due to a uniform magnetic field $B$ (perpendicular to the plane of the paper, as shown in the figure) in the vicinity of the wire. If the wire subtends an angle $2{\theta }_o$ at the center of the circle (of which it forms an arch) then the tension in the wire is: