The force acting on a current-carrying wire joining two fixed points $A$ and $B$ in a uniform magnetic field is:

$A$ square coil $ABCD$ of side $L$ is carrying a current $I_1$ in the clockwise direction. $A$ straight conductor carrying current $I_2$ (upward direction) is kept parallel to side $AB$ at a distance $\frac{L}{3}$ in the plane of $ABCD$. The net force on the coil $ABCD$ is ($\mu_0 =$ magnetic permeability).

The horizontal component of the Earth's magnetic field at a certain place is $3 \times 10^{-5} \, T$ and the direction of the field is from geographic south to geographic north. $A$ very long straight conductor is carrying a steady current of $1 \, A$. Calculate the force per unit length on it if the direction of the current is from east to west (in $N/m$).

$A$ $1\, m$ long wire is placed at right angles to a magnetic field. $A$ force of $1\, kg$ wt. acts on it in a magnetic field of $0.98\, T$. The current flowing through the wire is: (in $, A$)

$A$ long straight wire carrying a current of $25 \,A$ rests on a table. Another wire $PQ$ of length $1 \,m$ and mass $2.5 \,g$ carries the same current but in the opposite direction. The wire $PQ$ is free to slide up and down. To what height $h$ will wire $PQ$ rise (in $\,mm$)? (Take $g = 9.8 \,m/s^2$ and $\mu_0 = 4 \pi \times 10^{-7} \,T \cdot m/A$)

$A$ wire of length $L$ carries a current $I$ along the $X$-axis. The magnetic force acting on the wire is given by $\vec{F} = I B_0 L(\hat{k} - \hat{j})$. The existing magnetic field $\vec{B}$ is