Learning Goal: To apply the physics of the circular motion of charged particles

Question

Learning Goal:

To apply the physics of the circular motion of charged particles in a magnetic field.

A beam of high-energy particles can be useful for both scientific and commerical purposes. One machine designed to create such beams is called a particle accelerator.

One common type of accelerator is the cyclotron, as shown in the figure. (Figure 1) In a cyclotron, a magnetic field confines charged particles to circular paths while an oscillating electric field accelerates them. It is useful to understand the details of this process.

Consider a cyclotron in which a beam of particles of positive charge q and mass m is moving along a circular path restricted by the magnetic field B  (which is perpendicular to the velocity of the particles).

Part A:

Your goal is to accelerate the particles to kinetic energy K. What minimum radius R of the cyclotron is required?

Express your answer in terms of m, q, B, and K.?

Explanation / Answer

we know that

qvB = mV2/R

and

kinetic energy

K = mV2/2

V = sqrt (2K/m)

R = mV/qB

R = sqrt(2Km) /qB

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