$A$ loop of irregular shape carrying current is located in an external magnetic field. If the wire is flexible,it will take the shape of:

Two long conductors separated by a distance $d$ carry currents $I_1$ and $I_2$ in the same direction. They exert a force $F$ on each other. Now,the current in one of them is increased to $2$ times and its direction is reversed. The distance between them is also increased to $3d$. The new value of force between them is:

As shown in the figure, a metallic rod of linear density $0.45\,kg\,m^{-1}$ is lying horizontally on a smooth inclined plane which makes an angle of $45^{\circ}$ with the horizontal. The minimum current flowing in the rod required to keep it stationary, when a $0.15\,T$ magnetic field is acting on it in the vertical upward direction, will be $....A$ $\{$Use $g=10\,m/s^2\}$

$A$ straight wire is placed in a magnetic field that varies with distance $x$ from the origin as $\vec{B} = B_0 \left( 2 - \frac{x}{a} \right) \hat{k}$. The ends of the wire are at $(a, 0)$ and $(2a, 0)$ and it carries a current $I$ in the positive $x$-direction. If the force on the wire is $\vec{F} = IB_0 \left( \frac{ka}{2} \right) \hat{j}$, then the value of $k$ is:

$A$ rectangular coil $ABCD$ is hung from one side of a balance as shown in the figure. $A$ $500 \, g$ mass is added to the other arm to balance the weight of the coil. $A$ current of $9.8 \, A$ is passed through the coil and a constant magnetic field of $0.4 \, T$ acting inward is switched on such that only arm $CD$ of length $1.5 \, cm$ lies in the field. The additional mass $m$ that must be added to regain the balance is: (in $, g$)

$A$ wire is bent in the form of an equilateral triangle of side $100 \,cm$ and carries a current of $2 \,A$. It is placed in a magnetic field of induction $2.0 \,T$ directed perpendicular into the plane of paper. The direction and magnitude of magnetic force acting on each side of the triangle will be