A charged particle (charge q) is moving in a circle of radius R with uniform speed v. The associated magnetic moment μ is given by:

1. $\frac{qvR}{2}$

2. $qv{R}^2$

3. $\frac{qv{R}^2}{2}$

4. $qvR$

A bar magnet is hung by a thin cotton thread in a uniform horizontal magnetic field and is in the equilibrium state. The energy required to rotate it by 60^o is W. Now the torque required to keep the magnet in this new position is:

1.  $\frac{W}{\sqrt{3}}$

2.  

3.  

4.  

A millivoltmeter of 25 mV range is to be converted into an ammeter of 25 A range. The value (in ohm) of necessary shunt will be:

1. 0.001

2. 0.01

3. 1

4. 0.05

Two similar coils of radius R are lying concentrically with their planes at right angles to each other. The currents flowing in them are I and 2I, respectively. The resultant magnetic field induction at the center will be

1. $\frac{\sqrt{5}{\mu }_{0}I}{2R}$

2. $\frac{3{\mu }_{0}I}{2R}$

3. $\frac{{\mu }_{0}I}{2R}$

4. $\frac{{\mu }_{0}I}{R}$

Ionized hydrogen atoms and $\alpha$-particles with same momenta enters perpendicular to a constant magnetic field, B. The ratio of their radii of their paths $r_H:r_{\alpha }$ will be:

1. 1 : 4

2. 2 : 1

3. 1 : 2

4. 4 : 1

A metallic rod of mass per unit length 0.5 kg m^-1 is lying horizontally on a smooth inclined plane which makes an angle of 30° with the horizontal. The rod is not allowed to slide down by flowing a current through it when a magnetic field of induction 0.25 T is acting on it in the vertical direction. The current flowing in the rod to keep stationery is:

1. 7.14 A

2. 5.98 A

3. 14.76 A

4. 11.32 A

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. the force on the segment QP is: 
               

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 cylindrical conductor of radius R is carrying a constant current. Current is uniformly distributed in the cross-section. The plot of the magnitude of the magnetic field B with the distance d from the centre of the conductor, is correctly represented by the figure:

1. 

2. 

3. 

4.