Q. 315.0( 1 Vote )

A proton describes a circle of radius 1 cm is 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?

Given-
Radius of the circle, r = 1 cm

Magnetic field , B= 0.10 T

We know that the charge on a proton is e and that of an alpha

particle is 2e.

Also, the mass of a proton is m

Mass of an alpha particle is 4m.

let assume that both the particles are moving with speed v.

So, for the particle to move in a circle, the centrifugal force comes into acts which is provided by the magnetic force acting on it.

Also magnetic force, we know, Lorentz force F is given by -

where,

e = charge on an electron

v = velocity of the electron

B=magnetic field

Using the formula for centrifugal force

where,

v= velocity of the particle

r= radius of circle form

Equating the two forces, we will get-

Then, we can confer from question that-

Where

rp is the radius of the circle described by the proton which is 0.01

For alpha particle, radius is given by –

On dividing equation (1) by (2), we get:

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