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

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 , the net force on the remaining three arms of the loop is:

1. 3 $\overrightarrow{F}$

2. -$\overrightarrow{F}$

3. -3 $\overrightarrow{F}$

4.  $\overrightarrow{F}$

An electron is moving in a circular path under the influence of a transverse magnetic field of 3.57 x 10^-2 T. If the value of e/m is 1.76 x 10¹¹ C/kg, the frequency of revolution of the electron is:

1.  1 GHz

2.  100 MHz

3.  62.8 MHz

4.  6.28 MHz