A circular flexible loop of wire of radius $r$ carrying a current $I$ is placed in a uniform magnetic field $B$ perpendicular to the plane of the circle so that, wire comes under tension. If $B$ is doubled, tension in the loop

A conducting rod of length $L$ and mass $m$ is moving down a smooth inclined plane of inclination $\theta$ with constant speed $v$. A current $I$ is flowing in the conductor perpendicular to the paper inwards. A vertically upward magnetic field $B$ exists in space there. The magnitude of magnetic field $B$ is

A straight rod of mass $m$ and length $L$ is suspended from the identical springs as shown in figure. The spring is stretched a distance $x_{\circ }$ due to the weight of the wire.

The circuit has total resistance $R$. When the magnetic field perpendicular to the plane of paper is switched on, springs are observed to extend further by the same distance. The magnetic field strength is

A large metal sheet carries an electric current along its surface. Current per unit length is $\lambda$.

Magnetic field induction near the metal sheet is

Two straight infinitely long current-carrying wires are kept along $z$-axis at the coordinates $\left(0, a, 0\right)$ and $\left(0, -a, 0\right)$ respectively as shown in the figure. The current in each of the wire is equal and along negative $z$-axis (into the plane of the paper). The variation of the magnetic field on the $x$-axis will be approximately,