Question

In any experiment to measure ratio of radii of circular paths. Two
particles having charge 29 and q are projected with same speed
v. If the masses of particles are m and 2m respectively. If these
particles are projected perpendicularly in uniform magnetic field
B, then ratio of radii of their circular paths will be​

Answer 1

Answer:

Please note that we use the concept of Lorentz force here.

In order to find out the radii of a particle moving in a circular path as an effect of the magnetic field acting on it, we have-

mv²/ r= Bqv ( centripetal force= Lorentz force )

⇒ r= mv/ Bq

You can note this as a formula because we have to frequently refer to it to take ratios.

Now, we have charges q₁= 2q and q₂= q, masses m₁= m and m₂= 2m. v and B are constant, Ratio of radii= ?

r ∝ m/q

⇒ r₁/ r₂ = m₁/ m₂ × q₂/ q₁

⇒ r₁/ r₂ = m/ 2m × q/ 2q

⇒ r₁/ r₂ = 1/4