An alternating electric field of frequency v, 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=$\frac{mv}{e} and K=2m{\mathrm{\pi }}^2{\mathrm{v}}^2{\mathrm{R}}^2$

(2)B=$\frac{2\mathrm{\pi }mv}{e} and K=m^2{\mathrm{\pi vR}}^2$

(3)B=$\frac{2\mathrm{\pi }mv}{e} and K=2m{\mathrm{\pi }}^2{\mathrm{v}}^2{\mathrm{R}}^2$

(4)B=$\frac{mv}{e} and K=m^2{\mathrm{\pi vR}}^2$

A proton carrying 1 MeV kinetic energy is moving in a circular path of radius R in a uniform magnetic field. What should be the energy of an $\mathrm{\alpha }$-particle to describe a circle of the same radius in the same field?

1. 2 MeV                  2. 1 MeV

3. 0.5 MeV               4. 4 MeV

A current-carrying closed loop in the form of a right-angle isosceles triangle ABC is placed in a uniform magnetic field acting along AB. If the magnetic force on the arm BC is F, the force on the arm AC is:

1. $\mathbf{-}\mathbf{F}$                                               2. $\mathbf{F}$

3. $\sqrt{2}\mathbf{F}$                                             4. $-\sqrt{2}\mathbf{F}$

A galvanometer of resistance, G is shunted by a resistance S ohm. To keep the main current in the circuit unchanged, the resistance to be put in series with the galvanometer is

(1) $\frac{S^{\mathit{2}}}{(S+G)}$                                             

(2) $\frac{SG}{(S+G)}$

(3) $\frac{G^{\mathit{2}}}{(S+G)}$                                             

(4) $\frac{G}{(S+G)}$

A square loop, carrying a steady current I, is placed in a horizontal plane near a long straight conductor carrying a steady current $I_{\mathit{1}}$ at a distance d from the conductor as shown in figure. The loop will experience 

(1) a net repulsive force away from the conductor 

(2) a net torque acting upward perpendicular to the horizontal plane

(3) a net torque acting downward normal to the horizontal plane

(4) a net attractive force towards the conductor 

Charge q is uniformly spread on a thin ring of radius R. The ring rotates about its axis with a uniform frequency f Hz. The magnitude of magnetic induction at the center of the ring is :

(1) $\frac{{\mathrm{\mu }}_0\mathrm{q} f}{2\mathrm{R}}$                                       

(2) $\frac{{\mathrm{\mu }}_0\mathrm{q}}{2f\mathrm{R}}$

(3) $\frac{{\mathrm{\mu }}_0\mathrm{q}}{2\mathrm{\pi }f\mathrm{R}}$                                       

(4) $\frac{{\mathrm{\mu }}_0\mathrm{q} f}{2\mathrm{\pi R}}$

A beam of cathode rays is subjected to crossed Electric (E) and magnetic fields(B). The fields are adjusted such that the beam is not deflected. The specific charge of the cathode rays is given by:

1. $\frac{B^2}{2V{E}^2}$                                             

2. $\frac{2V{B}^2}{E^2}$

3. $\frac{2V{E}^2}{B^2}$                                           

4. $\frac{E^2}{2V{B}^2}$

(where V is the potential difference between cathode and anode)

A galvanometer has a coil of resistance $100\Omega$ and gives a full scale deflection for 30 mA current.If it is to work as a voltmeter of 30V range, the resistance required to be added will be 

(1) 900 $\Omega$                                     

(2) 1800 $\Omega$

(3) 500 $\Omega$                                     

(4) 1000 $\Omega$

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 $\overrightarrow{F}$, the net force on the remaining three arms of the loop is

1. 3$\overrightarrow{F}$                 

2. $-$$\overrightarrow{F}$

3. $-$3$\overrightarrow{F}$               

4.  $\overrightarrow{F}$