$A$ semi-circular current-carrying wire having radius $R$ is placed in the $x-y$ plane with its centre at the origin $O$. $A$ non-uniform magnetic field $\vec B = \frac{B_o x}{2R} \hat k$ (where $B_o$ is a positive constant) exists in the region. The magnetic force acting on the semi-circular wire will be along:

Two long wires with no contact are placed perpendicular to each other. $i_1$ and $i_2$ are currents flowing through these wires respectively. The magnetic force on a small length '$d$' of the second wire situated at a distance '$l$' from the first wire is proportional to,

Define $1 \ A$ (Ampere) using the force between two current-carrying parallel wires.

An arrangement of three parallel straight wires placed perpendicular to the plane of the paper carrying the same current $I$ along the same direction is shown in the figure. The magnitude of the force per unit length on the middle wire $B$ is given by:

$A$ wire $X$ of length $50 \; cm$ carrying a current of $2 \; A$ is placed parallel to a long wire $Y$ of length $5 \; m$. The wire $Y$ carries a current of $3 \; A$. The distance between the two wires is $5 \; cm$ and the currents flow in the same direction. The force acting on the wire $X$ due to wire $Y$ is:

$A$ single turn current loop in the shape of a right-angled triangle with sides $5\,cm$,$12\,cm$,and $13\,cm$ carries a current of $2\,A$. The loop is placed in a uniform magnetic field of magnitude $0.75\,T$,whose direction is parallel to the current in the $13\,cm$ side of the loop. The magnitude of the magnetic force on the $5\,cm$ side is $\frac{x}{130}\,N$. The value of $x$ is $..........$