Q31 of 91 Page 230

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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