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?
Answer :
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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