Question

The velocities of two alpha particles entering a uniform magnetic field are in the ratio of 4:1.What is the ratio of the radii of their circular path?

Answer 1

we know that in this case

magnetic force = centripetal force

so,

qvB = mv²/r

or the radius will be

r = mv / qB

so,

for particle 1

r₁ = mv₁ / qB

and

for particle 2

r₂ = mv₂ / qB

or

the ratio

r₁ / r₂ = [ mv₁ / qB] / [ mv₂ / qB]

or

r₁ / r₂ = v₁ / v₂

now as

v₁ / v₂ = 4/1

thus,

r₁ / r₂ = 4 / 1