A rectangular coil of length \(0.12~\text{m}\) and width \(0.1~\text{m}\) having \(50\) turns of wire is suspended vertically in a uniform magnetic field of strength \(0.2~\text{Wb/m}^2\). The coil carries a current of \(2~\text{A}\). If the plane of the coil is inclined at an angle of \(30^{\circ}\) with the direction of the field, the torque required to keep the coil in stable equilibrium will be:
1. \(0.15~\text{N-m}\)
2. \(0.20~\text{N-m}\)
3. \(0.24~\text{N-m}\)
4. \(0.12~\text{N-m}\)

A square loop, carrying a steady current I, is placed in a horizontal plane near a long straight conductor carrying a steady current I1 at a distance d from the conductor as shown in the figure. The loop will experience:

A closed-loop \(PQRS\) carrying a current is placed in a uniform magnetic field. If the magnetic forces on segments \(PS\), \(SR,\) and \(RQ\) are \(F_1, F_2~\text{and}~F_3\) respectively, and are in the plane of the paper and along the directions shown, then which of the following forces acts on the segment \(QP\)?
        

1. \(F_{3} - F_{1} - F_{2}\)

2. \(\sqrt{\left(F_{3} - F_{1}\right)^{2} + F_{2}^{2}}\)

3. \(\sqrt{\left(F_{3} - F_{1}\right)^{2} - F_{2}^{2}}\)

4. \(F_{3} - F_{1} + F_{2}\)