Question

A proton describes a circle of radius 1 cm in a magnetic field of strength 0.10 T. What would be the radius of the circle described by an α-particle moving with the same speed in the same magnetic field?

Answer 1

Explanation:

It is given that the circle’s radius is r = 1 cm.

Magnetic field = 0.10 T

It is known that the proton’s charge is e and the alpha particle’s charge is 2e. And, the mass of the alpha particle is 4m and that of proton is m.

Assume that both the particles are moving with v speed. As per the information provided in the question,  

rp = mveB, where the circle’s radius is shown as rp defined by the proton.

0.01 = mve $\times$ 0.1    …(i)  

rα = 4mv2eBrα = 4mv2e $\times$ 0.1    …(ii)

When equation (ii) is divided by (i), we obtain:

rα=0.02 m=2 cm