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

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

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

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

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

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

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

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

What is the primary function of the electric field in a cyclotron?

1. energize the charged particle.

2. bring the charged particle again and again into the field.

3. cancel the force due to the magnetic field.

4. guide charged particles to the exit part.

Which of the following statements about cyclotron is correct?

Suppose a cyclotron is operated at an oscillator frequency of 12 MHz and a discharge radius of 53 cm. What is the resulting kinetic energy of the deuterons?
(Mass of deuteron, \(m=3.34\times10^{-27}\) kg)

1. 16.6 MeV
2. 12 MeV
3. 15 MeV
4. 14 MeV

A monoenergetic electron beam with an electron speed of 5.20 x 10⁶ m/s is subject to a magnetic field of 1.30 x 10^-4 T normal to the beam velocity. What is the radius of the circle traced by the beam, given e/m for electron equals 1.76 x 10¹¹ C kg^-1?

1. 22.7 cm
2. 21.3 cm
3. 20.0 cm
4. 21.9 cm

An electron gun with its collector at a potential of 100 V fires out electrons in a spherical bulb containing hydrogen gas at low pressure $\left(~{10}^{-2} mm of Hg\right).$ A magnetic field of $2.83\times {10}^{-4} T$ curves the path of the electrons in a circular orbit of radius 12.0 cm. (The path can be viewed because the gas ions in the path focus the beam by attracting electrons, and emitting light by electron capture; this method is known as the 'fine beam tube' method. Specific charge ratio (e/m) is:
1. \(1.21 \times 10^{11} \mathrm{C}~ \mathrm{kg}^{-1}\)
2. \(1.73 \times 10^{11} \mathrm{C}~\mathrm{kg}^{-1}\)
3. \(2.53 \times 10^{11} \mathrm{C}~\mathrm{kg}^{-1}\)
4. \(3.02 \times 10^{11} \mathrm{C}~\mathrm{kg}^{-1}\)

In a cyclotron, a charged particle:
 

A cyclotron’s oscillator frequency is 10 MHz. The radius of its ‘dees’ is 60 cm, what should be the operating magnetic field for accelerating protons and the kinetic energy (in MeV) of the proton beam produced by the accelerator?

1. 0.66 T, 6 MeV

2. 0.33 T, 6 MeV

3. 0.66 T, 7 MeV

4. 0.33 T, 7 MeV

A particle is projected in a plane perpendicular to a uniform magnetic field. The area bounded by the path described by the particle is proportional to 

1.   the velocity

2.   the momentum

3.   the kinetic energy

4.   none of these