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 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 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 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 magnetic dipole is under the influence of two magnetic fields. The angle between the field directions is 60°, and one of the fields has a magnitude of 1.2×10^-2 T. If the dipole comes to stable equilibrium at an angle of 15° with this field, what is the magnitude of the other field?
 \(\left[\text{Given} :   \sin   15^ \circ = 0 . 26\right]\)
1. \( 7.29 \times10^{-3} ~\mathrm{T} \)
2. \( 4.39 \times10^{-3} ~\mathrm{T} \)
3. \( 6.18 \times10^{-3} ~\mathrm{T} \)
4. \(5.37 \times10^{-3} ~\mathrm{T} \)

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

A circular loop with a radius of 20 cm is placed in a uniform magnetic field B = 2T in the XY plane as shown in the figure. If the loop carries a current of i = 1 A, then the magnitude of torque acting on the loop will be:
       
1.  0.25 N-m

2.  5.2 N-m

3.  2.5 N-m

4.  0.52 N-m

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 closed-loop (of any shape) carrying current lies in the x-y plane. What happens when a uniform magnetic field B is present in the region such that the loop experiences zero force?

Two insulated rings, one of a slightly smaller diameter than the other, are suspended along their common diameter as shown. Initially, the planes of the rings are mutually perpendicular. What happens when a steady current is set up in each of them?