$A$ wire carrying a current $I$ is placed inside a uniform magnetic field $\vec{B} = -B_0 \hat{k}$. The shape of the wire is parabolic and has the equation $y = 2x - x^2$. The force on the wire will be:

$A$ conducting bar $PQ$ of length $l$ carrying current $I$ is suspended from a rigid support as shown in the figure. $A$ uniform magnetic field $B$ perpendicular to $PQ$ and directed away from the reader (into the plane) is applied. If the mass of the bar is $M$,find the tension in each string.

$A$ $3.0 \; cm$ wire carrying a current of $10 \; A$ is placed inside a solenoid perpendicular to its axis. The magnetic field inside the solenoid is given to be $0.27 \; T$. What is the magnetic force on the wire?

The magnetic field existing in a region is given by $\vec B = B_0 \left( 5 + \frac{x}{l} \right) \hat k$. $A$ square loop of edge $l$ and carrying a current $i$ is placed with its edges parallel to $x-y$ axes. Find the magnitude of the net magnetic force experienced by the loop.

What is the force per unit length between the two wires shown in the figure? [${\mu _0} = 4\pi \times {10^{ - 7}} \text{ T}\,m/A$]

$A$ massless square loop of wire with resistance $10\,\Omega$ supports a mass of $1\,g$. It hangs vertically with one of its sides in a uniform magnetic field of $10^3\,G$,directed outwards in the shaded region. $A$ $DC$ voltage $V$ is applied to the loop. For what value of $V$ will the magnetic force exactly balance the weight of the supporting mass of $1\,g$? (Given: side length of the loop $= 10\,cm$,$g = 10\,m/s^2$)