A \(250\) turn rectangular coil of length \(2.1\) cm and width \(1.25\) cm carries a current of \(85~\mu\text{A}\) and subjected to the magnetic field of strength \(0.85~\text{T}\). Work done for rotating the coil by \(180^\circ\) against the torque is:
1. \(4.55~\mu\text{J} \)
2. \(2.3~\mu\text{J} \)
3. \(1.15~\mu\text{J} \)
4. \(9.4~\mu\text{J} \)

If a square loop \(\text{ABCD}\) carrying a current \(i\) is placed near and coplanar with a long straight conductor \(\mathrm{XY}\) carrying a current \(I\), what will be the net force on the loop?
               
1. \(\frac{\mu_0Ii}{2\pi}\)
2. \(\frac{2\mu_0IiL}{3\pi}\)
3. \(\frac{\mu_0IiL}{2\pi}\)
4. \(\frac{2\mu_0Ii}{3\pi}\)

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 current-carrying closed loop in the form of a right isosceles triangle ABC is placed in a uniform magnetic field acting along with AB.  If the magnetic force on the arm BC is F, then what is the force on the arm AC?
                

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 square current-carrying loop is suspended in a uniform magnetic field acting in the plane of the loop. If the force on one arm of the loop is \( \overrightarrow{F}\), what will be the net force on the remaining three arms of the loop? 

A closely wound solenoid of 2000 turns and an area of cross-section of 1.5 × 10^–4 m² carries a current of 2.0 A. It is suspended through its centre and perpendicular to its length, allowing it to turn in a horizontal plane in a uniform magnetic field of 5 × 10^–2 Tesla, making an angle of 30^o with the axis of the solenoid. What will be the torque on the solenoid?

1. 1.5 × 10^–3 Nm

2. 1.5 × 10^–2 Nm

3. 3 × 10^–2 Nm

4. 3 × 10^–3 Nm

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 F₁, F_2, and F₃ 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. ${\mathrm{F}}_3-{\mathrm{F}}_1-{\mathrm{F}}_2$

2. $\sqrt{{\left({\mathrm{F}}_3-{\mathrm{F}}_1\right)}^2+{\mathrm{F}}_2^2}$

3. $\sqrt{{\left({\mathrm{F}}_3-{\mathrm{F}}_1\right)}^2-{\mathrm{F}}_2^2}$

4. ${\mathrm{F}}_3-{\mathrm{F}}_1+{\mathrm{F}}_2$

A coil in the shape of an equilateral triangle of side l is suspended between the pole pieces of a permanent magnet such that $\overrightarrow{\mathrm{B}}$ is in the plane of the coil. If due to a current i in the triangle, a torque τ acts on it, the side l of the triangle will be:

1. $\frac{2}{\sqrt{3}}\left(\frac{\tau }{\mathrm{Bi}}\right)$ $$

2. $\frac{1}{\sqrt{3}}\frac{\tau }{\mathrm{Bi}}$

3. $2{\left(\frac{\tau }{\sqrt{3}\mathrm{Bi}}\right)}^{\frac{1}{2}}$

4. $\frac{2}{\sqrt{3}}{\left(\frac{\tau }{\mathrm{Bi}}\right)}^{\frac{1}{2}}$