$A$ current-carrying wire $LN$ is bent as shown below. If the wire carries a current of $10 \, A$ and is placed in a magnetic field of $5 \, T$ which acts perpendicular to the paper outwards,then it will experience a force of ......... $N$.

$A$ wire carrying a current $I$ along the positive $x$-axis has length $L$. It is kept in a magnetic field $\overrightarrow{B} = (2\hat{i} + 3\hat{j} - 4\hat{k}) \text{ T}$. The magnitude of the magnetic force acting on the wire is $..........IL$.

$A$ 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:

Write the magnetic force equation on a current-carrying element $I\vec{dl}$ inside a magnetic field $\vec{B}$. Write the law used to determine the direction of the magnetic force.

$A$ horizontal rod of mass $10 \, g$ and length $10 \, cm$ is placed on a smooth plane inclined at an angle of $60^\circ$ with the horizontal,with the length of the rod parallel to the edge of the inclined plane. $A$ uniform magnetic field of induction $B$ is applied vertically downwards. If the current through the rod is $1.73 \, A$,then the value of $B$ for which the rod remains stationary on the inclined plane is......$T$

$A$ 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 $\mu_0 = 4 \pi \times 10^{-7} \,T \cdot m/A$)