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

Two circular coils 1 and 2 are made from the same wire but the radius of the 1^st coil is twice that of the 2^nd coil. What is the ratio of the potential difference applied across them so that the magnetic field at their centres is the same?

1. 3

2. 4

3. 6

4. 2

An alternating electric field of frequency $\nu$, is applied across the dees (radius=R) of a cyclotron that is being used to accelerate protons (mass=m). The operating magnetic field B, used in the cyclotron and the kinetic energy (K) of the proton beam, produced by it, are given by:

1. $B=\frac{m\nu }{e}and K=2m{\mathrm{\pi }}^2{\mathrm{\nu }}^2{\mathrm{R}}^2$

2. $B=\frac{2\mathrm{\pi }m\nu }{e}and K=m^2\pi \nu R^2$

3. $B=\frac{2\mathrm{\pi }m\nu }{e}and K=2m{\mathrm{\pi }}^2{\mathrm{\nu }}^2{\mathrm{R}}^2$

4. $B=\frac{m\nu }{e}and K=m^2\pi \nu R^2$

A straight conductor carrying current I splits into two parts as shown in the figure. The radius of the circular loop is R. The total magnetic field at the centre P of the loop is,

(1)  zero

(2) $\frac{3{\mu }_{0}i}{32R}, inward$

(3) $\frac{3{\mu }_{0}i}{32R}, outward$

(4) $\frac{{\mu }_{0}i}{2R}, inward$