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

Given:
Radius of the circle, r = 1 cm
Magnetic field = 0.10 T
We know that the charge of a proton is e and that of an alpha particle is 2e. Also, the mass of a proton is m and that of an aplha particle is 4m. 
Suppose, both the particles are moving with speed v.
According to the question,
`r_p =(mv)/(eB),` where r_p is the radius of the circle descrinbed by the proton.
0.01 = `(mv)/(exx00.1)`

`r_a = (4mv)/(2eB)`

`r_a = (4mv)/(2eB)`............(ii)
On dividing equation (ii) by (i), we get:

`(ra)/0.01 = ((4mvxxexx0.1)/(2exx0.1xxmv))`
`r_a = 0.02 m =2 cm`