Question

An electron and a proton, having equal momenta, enter a uniform magnetic field at right angles to the field lines. What will be the ratio of their trajectories? (

Answer 1

Momentum of both electron and proton are equal. - (Given)

Then , P = mv is (constant).

We know that,

F = q v B sin θ.

(Here , F - force, q - charge, v - velocity, B - magnetic field)

This force provides the required centripetal force for the motion along circular path whose radius is r.

Centripetal force = [math]\frac{mv^2}{r}[/math]

Then,

[math]\frac{mv^2}{r} = qvB sin\theta [/math]

Here, θ = 90 degrees .

Then,

[math]r= \frac{mv}{Bq}= 1 : 1[/math]