A ring of radius R carries a linear charge density $\lambda$. It is rotating with angular speed $\omega$ about an axis passing through the centre and perpendicular to the plane. What is the magnetic field at its centre?

1.  $\frac{3{\mu }_0\lambda \omega }{2}$

2.  $\frac{{\mu }_0\lambda \omega }{2}$

3.  $\frac{{\mu }_0\lambda \omega }{\pi }$

4.  ${\mu }_0\lambda \omega$  

The figure depicts a cross-section of a large metal sheet with an electric current flowing along its surface. The current in a dl-width strip is (Kdl), where K is a constant. What is the magnetic field at a point P and at a distance x from the metal strips?
    
1.  $\frac{1}{2}{\mu }_{0}Kx$

2.  ${\mu }_{0}K$

3.  $\frac{1}{2}{\mu }_{0}K$

4.  $\frac{{\mu }_{0}Kx}{4}$

1. 0.25 amp

2. 0.8 amp

3. 0.2 amp

4. 0.5 amp

The current sensitivity of a moving coil galvanometer is 5 div/mA and its voltage sensitivity (angular deflection per unit voltage applied) is 20 div/V. How much is the resistance of the galvanometer?

Perpendicularly, an electron and a proton enter a magnetic field. Both have the same amount of kinetic energy. Which of the following statements is correct?

A particle having a mass of ${10}^{-2}$ $\mathrm{kg}$ $$carries a charge of $5\times {10}^{-8}$ $\mathrm{C}.$ The particle is given an initial horizontal velocity of ${10}^5$ ${\mathrm{ms}}^{-1}$ in the presence of an electric field $\overrightarrow{\mathbf{E}}$ and magnetic field $\overrightarrow{\mathbf{B}}$. How can we keep the particles moving in a horizontal direction?

Which one of the following pairs of statements are possible?
1. a and c 
2. c and d
3. b and c
4. b and d

A long solenoid has 800 turns per metre of the length of the solenoid. A current of 1.6 A flows through it. What is the magnetic induction at the end of the solenoid on its axis?

A cell is connected between the points A and C of a circular conductor ABCD of centre O with an angle of AOC = 60°.
If B₁ and B₂ are the magnitudes of the magnetic fields at O due to the currents in ABC and ADC respectively, the ratio B₁: B₂ will be:        
     

1. 0.2                             

2. 6                                    

3. 1

4. 5                    

What is the result of an electric charge in uniform motion?

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. $\frac{q}{\mathrm{\pi m}}$