Question

Solve this:
25. An alternate 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 filed (B) used in the cyclotron and the kinetic energy (K) f the proton beam, produced by it, given by
$$\begin{gathered} 1)B=\frac{2\mathrm{\pi mv}}{e}andK=2m{\mathrm{\pi }}^2{\mathrm{v}}^2{\mathrm{R}}^2 \\ 2)\mathrm{B}=\frac{\mathrm{mv}}{\mathrm{e}}\mathrm{and}\mathrm{K}={\mathrm{m}}^2{\mathrm{\pi vR}}^2 \\ 3)\mathrm{B}=\frac{\mathrm{mv}}{\mathrm{e}}\mathrm{and}\mathrm{K}=2{\mathrm{m\pi }}^2{\mathrm{v}}^2{\mathrm{R}}^2 \\ 4)\mathrm{B}=\frac{2\mathrm{\pi mv}}{\mathrm{e}}\mathrm{and}\mathrm{K}={\mathrm{m}}^2{\mathrm{\pi vR}}^2 \end{gathered}$$

Answer 1

Dear Student ,
$$\begin{gathered} Frequency=\nu =\frac{eB}{2\pi m} \\ So,B=\frac{2\pi m\nu }{e} \\ KineticenergyK=\frac{1}{2}m{v}^2 \\ radiusR=\frac{mv}{eB} \end{gathered}$$


Regards