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. 

A long wire carrying a steady current is bent into a circular loop of one turn. The magnetic field at the centre of the loop is B. It is then bent into a 
circular coil of n turns. The magnetic field at the centre of this coil of n turns will be:

1.  nB

2.  n²B

3.  2nB

4.  2n²B

In a mass spectrometer used for measuring the masses of ions, the ions are initially accelerated by an electric potential V and then made to describe semi-circular paths of radius R using a magnetic field B. If V and B are kept constant, the ratio $\frac{Charge on the ion}{mass of the ion}$, will be proportional to:

1. $\frac{1}{R}$

2. $\frac{1}{R^2}$

3. $R^2$

4. R