Question

A cyclotron (Fig. 29.16) designed to accelerate protons has an outer radius of 0.350 m . The protons are emitted nearly at rest from a source at the center and are accelerated through 600 V each time they cross the gap between the dees. The dees are between the poles of an electromagnet where the field is 0.800 T .(c) their maximum kinetic energy.

Answer 1

The Maximum Kinetic energy of a proton is -

E(max) = 0.063 x $10^{11}$ joules.

We have a Cyclotron designed to accelerate protons.

We have to determine the Maximum Kinetic energy of Protons.

What is a Cyclotron? On what principle it works?

Cyclotron is a device used to accelerate charged particles to high energies. It works on the principle that a charged particle moving normal to a magnetic field experiences magnetic Lorentz force due to which the particle moves in a circular path. The magnetic Lorentz force is given by-

F = qvB sinθ

According to the question -

In a cyclotron the force by a magnetic field is equal to the centrifugal force.

Now, for r(max) -                                     ( Since v = rω)

q v(max) B sin (90) = $\frac{m\times v(max)^{2} }{r(max)}$

$v(max)=\frac{qBr(max)}{m}$

Now -

r(max) = 0.35 m

B = 0.8 Tesla

Therefore -

v(max) = $\frac{1.6\times 10^{-19} \times 0.8 \times 0.35}{1.6\times 10^{-27} }$

v(max) = 0.28 x $10^{8}$ m/sec

Therefore, the Maximum kinetic energy =

E(max) = $\frac{1}{2} m\times v(max)^{2}$

E(max) = $\frac{1}{2} \times 1.6\times 10^{-27} \times 0.28\times 10^{8} \times 0.28\times 10^{8}$

E(max) = 0.063 x $10^{11}$ joules

Hence, the Maximum Kinetic energy of a proton is -

E(max) = 0.063 x $10^{11}$ joules.

To solve more questions on Cyclotron, visit the link below-

brainly.com/question/14555284

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