Question

A charged particle is observed traveling in a circular path of radius R in a uniform magnetic field. If the particle were traveling twice as fast, the radius of the circular path would be:

Answer 1

Answer:

radius of circular path becomes doubled

Explanation:

As the charged particle is moving in a magnetic field then it experiences a centripetal force.

So, the magnetic force is balanced by the centripetal force

$q\times v\times B = \frac{mv^{2}}{R}$

where, m be the mass of charged particle, q be the charge and v be the velocity, B be the magnetic field, R be the radius of circular path.

$R = \frac{mv}}{qB}$

Here we observe that the radius of the path is directly proportional to the velocity of the charged particle.

R ∝ v    ..... (1)

let the new radius be R' as the velocity is doubled

R' ∝ 2 v    ..... (2)

Divide equation (2) by equation (1) we get

R' = 2 R

Thus, the radius of circular path becomes doubled.