A charge $\text{'}q\text{'}$ is accelerated through a potential difference,$V$ It is then passed normally through a uniform magnetic field, where it moves in a circle of radius $\text{'}r\text{'}$. The potential difference required to move it in a circle of radius $2r$ is,

A charged particle is moving in a uniform magnetic field in a circular path. Radius of circular path is $\mathrm{R}$. When energy of particle is doubled, then new radius will be 

An electron having mass $9.1\times {10}^{-31} \mathrm{kg}$, charge $1.6\times {10}^{-19} \mathrm{C}$ and moving with the velocity of ${10}^6 \mathrm{m} {\mathrm{s}}^{-1}$ enters a region where a magnetic field exists. If it describes a circle of radius $0.2 \mathrm{m}$ then the intensity of the magnetic field must be $\times {10}^{-5} \mathrm{T}$.

A proton beam enters a magnetic field of ${10}^{-4} \mathrm{Wb} {\mathrm{m}}^{-2}$ normally. If the specific charge of the proton is ${10}^{11} \mathrm{C} {\mathrm{kg}}^{-1}$and its velocity is ${10}^9 \mathrm{m} {\mathrm{s}}^{-1}$, then the radius of the circle described will be

The ratio of periods of $\alpha$-particle and proton moving on a circular path in a uniform magnetic field is,

A proton of mass $\text{'}m\text{'}$ moving with a speed $v$($<<c$ the velocity of light in vacuum) completes a circular orbit in time, $T$ in a uniform magnetic field. If the speed of the proton is increased to $\sqrt{2}v$ what will be the time needed to complete the circular orbit?

The maximum velocity to which a proton can be accelerated in a cyclotron of $10 \mathrm{MHz}$ frequency and radius $50 \mathrm{cm}$ is

The cyclotron frequency of an electron grating in a magnetic field of $1$ $\mathrm{T}$ is approximately ___$\left(e=1.6\times {10}^{-19} \mathrm{C}, m_e=9.1\times {10}^{-31} \mathrm{Kg}\right)$

A cyclotron's oscillator frequency is $10 \mathrm{MHz}$ and the operating magnetic field is $0.66 \mathrm{T}$. If the radius of its dees is $60 \mathrm{cm},$ then the kinetic energy of the proton beam produced by the accelerator is,