JEE Main & Advanced Physics Magnetic Effects of Current / करंट का चुंबकीय प्रभाव Cyclotron

Cyclotron is a device used to accelerated positively charged particles (like, a-particles, deutrons etc.) to acquire enough energy to carry out nuclear disintegration etc. It is based on the fact that the electric field accelerates a charged particle and the magnetic field keeps it revolving in circular orbits of constant frequency.

It consists of two hollow D-shaped metallic chambers \[{{D}_{1}}\] and \[{{D}_{2}}\] called dees. The two dees are placed horizontally with a small gap separating them. The dees are connected to the source of high frequency electric field. The dees are enclosed in a metal box containing a gas at a low pressure of the order of \[{{10}^{-3}}\] mm mercury. The whole apparatus is placed between the two poles of a strong electromagnet NS as shown in fig. The magnetic field acts perpendicular to the plane of the dees.

(1) Cyclotron frequency : Time taken by ion to describe a semicircular path is given by \[t=\frac{\pi \,r}{v}=\frac{\pi \,m}{qB}\] If \[T=\] time period of oscillating electric field then \[T=2t=\frac{2\pi \,m}{qB}\] the cyclotron frequency \[\nu =\frac{1}{T}=\frac{Bq}{2\pi m}\]

(2) Maximum energy of particle : Maximum energy gained by the charged particle \[{{E}_{\max }}=\left( \frac{{{q}^{2}}{{B}^{2}}}{2m} \right)\,{{r}^{2}}\] where \[{{r}_{0}}=\] maximum radius of the circular path followed by the positive ion.