Question

The angular speed of a charged particle of charge q and mass m in a magnetic field b
is?

Answer 1

Answer:

The angular speed of a charged particle  will be ω = qb/m

Explanation:

Given data,

charge of the particle = q

mass of the particle = m

strength of the magnetic field = b

let v and r be the linear velocity and radius of the circular path,

The magnetic force acting on the particle,

F = qvb

To move in a circular path, the centripetal force acting on the particle will be

F = mv²/r

both these force should be equal to each other

=> qvb = mv²/r

=> qb = m(v/r)

but we know that the angular velocity is given as,

ω = v/r

=> qb = mω

=> ω = qb/m

Hence the angular speed of a charged particle  will be ω = qb/m