Question

A cyclotron is used to accelerate charged particles, Then the time period under the
influence of 1T magnetic field of a proton: -
A. \[20\pi \,ns\]
B. \[40\pi \,ns\]
C. \[10\pi \,ns\]
D. \[5\pi \,ns\]

Answer 1

Hint: A cyclotron quickens a charged molecule bar utilizing a high recurrence rotating voltage which is applied between two empty "D"- molded sheet metal terminals called "dees" inside a vacuum chamber.
The dees are put up close and personal with a tight hole between them, making a round and hollow space inside them for the particles to move.

Complete step-by-step answer:
The correct option is A.
\[T=\dfrac{2\pi m}{qB}\]
\[T=\dfrac{2\pi }{1}\left( \dfrac{m}{q} \right)\]
\[T=\dfrac{2\pi }{9.6\times {{10}^{7}}}\]
\[T=20\pi \times {{10}^{-9}}sec\]
\[T=20\pi nsec\]

The particles are infused into the focal point of this space. The dees are situated between the shafts of an enormous electromagnet which applies a static attractive field B opposite to the cathode plane. The attractive field makes the particles' way twist in a hover because of the Lorentz force opposite to their heading of motion.
If the particles' paces were consistent, they would go in a round way inside the dees affected by the attractive field. Anyway, a radio recurrence (RF) exchanging voltage of a few thousand volts is applied between the dees. The voltage makes a swaying electric field in the hole between the dees that quickens the particles.
The recurrence is set with the goal that the particles make one circuit during a solitary pattern of the voltage. To accomplish this, the recurrence must match the molecule's cyclotron reverberation recurrence where B is the attractive field quality, q is the electric charge of the molecule and m is the relative mass of the charged molecule. Each time after the particles go to the next dee cathode the extremity of the RF voltage turns around. In this manner, each time the particles cross the hole from one dee terminal to the next, the electric field is in the right course to quicken them.

Note: The particles' speeding up because of these pushes makes them move in a bigger span hover with every revolution, so the particles move in a winding way outward from the middle to the edge of the dees. At the point when they arrive at edge a little voltage on a metal plate diverts the shaft so it leaves the dees through a little hole among them, and hits an objective situated at the leave point at the edge of the chamber, or leaves the cyclotron through a cleared bar cylinder to hit a far off objective.
Different materials might be utilized for the objective, and the atomic responses because of the collisions will make auxiliary particles which might be guided outside of the cyclotron and into instruments for examination.