If the planes of two identical concentric coils are perpendicular and the magnetic moment of each coil is \(\mathrm M,\) then the resultant magnetic moment of the two-coil system will be:

A charge Q is uniformly distributed on a ring of radius R made of an insulating material. If the ring rotates about the axis passing through its centre and normal to the plane of the ring with constant angular speed ω, then what will be the magnitude of the magnetic moment of the ring?

1. $Q\omega R^2$
2. $\frac{1}{2}Q\omega R^2$
3. $Q{\omega }^{2}R$
4. $\frac{1}{2}Q{\omega }^{2}R$

Two particles each of mass m and charge q are attached to the two ends of a light rigid rod of length 2R. The rod is rotated at constant angular speed about a perpendicular axis passing through its centre. What is the ratio of the magnitudes of the magnetic moment of the system and its angular momentum about the centre of the rod?

1. $\frac{q}{2m}$                               

2. $\frac{q}{m}$

3. $\frac{2q}{m}$                              

4. $\frac{q}{\mathrm{\pi m}}$ 

The two parts of the loop are circles of radii 2a and a, respectively, and carry the same current i as shown in the given figure. What is the magnitude of the dipole moment of the current loop?

1. $5{\mathrm{\pi a}}^2$ $\mathrm{i}$

2. $4{\mathrm{\pi a}}^2$ $\mathrm{i}$

3. $3{\mathrm{\pi a}}^2$ $\mathrm{i}$

4. Zero

If a charged particle (charge q) is moving in a circle of radius R at a uniform speed v, then the value of its associated magnetic moment μ will be:

1. $\frac{\mathrm{qvR}}{2}$

2. ${\mathrm{qvR}}^2$

3. $\frac{{\mathrm{qvR}}^2}{2}$

4. $\mathrm{qvR}$

A wire of length \(L\) meters carrying a current of \(I\) amp is bent in the form of a circle. What is its magnetic moment?
1. \( \frac{{IL}^2}{4} ~\text{A}\text-\text{m}^2 \)
2. \( \frac{{I} \times \pi {L}^2}{4} ~\text{A}\text-\text{m}^2 \)
3. \( \frac{2 {IL}^2}{\pi}~\text{A}\text-\text{m}^2 \)
4. \( \frac{{IL}^2}{4 \pi}~\text{A}\text-\text{m}^2 \)

What is the magnetic moment of the following current loop?
 
1. $24$ $A{m}^2$

2. $12$ $A{m}^2$

3. $6$ $A{m}^2$

4. Zero

In a hydrogen atom, the electron makes 6.6×10¹⁵ rev/sec around the nucleus in an orbit of radius 0.528 Å. What will (A-m²) its magnetic moment be?
1. $1\times {10}^{-15}$                     

2. $1\times {10}^{-10}$

3. $1\times {10}^{-23}$                      

4. $1\times {10}^{-27}$

A wire of length l carrying current i is folded to form a circular coil of N turns. What should be the value of N to have the maximum value of the magnetic moment in the coil?

1. 1

2. 4

3. 9

4. 10

What is the magnetic dipole moment of the given loop?