Question

The radius of curvature of the path of a charged particle in a uniform magnetic field is directly proportional toA) the particle's charge.B) the particle's momentum.C) the particle's energy.D) the flux density of the field.E)All of these are correct

Answer 1

B) the particle's momentum.

Step-by-step explanation:

We know that

The centripetal force on the particle when its moving in the radius R and velocity V

`F_c=(m* V^2)/(R)`

The magnetic force on the particle when the its moving with velocity V in the magnetic filed B and having charge q

`F_m=q* V* B`

At the equilibrium condition

`F_m=F_c`

`q* V* B=(m* V^2)/(R)`

`R=(m* V)/(q* B)`

Momentum = m V

Therefore we can say that the radius of curvature is directly proportional to the particle momentum.

B) the particle's momentum.