Question

A charge enters a uniform magnetic field oriented perpendicular to its path. The field deflects the particle into a circular arc of radius R. If the charged particle enters the same magnetic field with three times the speed, what will be the radius of the circular arc?

Answer 1

Answer:

The new radius is three times the initial radius

Explanation:

The magnetic force is given by the equation

      F = q v x B

Where the blacks indicate vectors, q is the electric charge, v the velocity of the particle and B the magnetic field. The scalar magnitude of this force is

     F = q v B sin θ

Where θ is the angle between the velocity and the magnetic field.

As the force is perpendicular to the velocity, the particle describes a circular motion, using Newton's second law we can find the acceleration that is centripetal.

    F = ma

    a = v² / r

   

   q v B = mv² / r

  R = mv / qB

Let's calculate for the new speed (v₂ = 3v)

  R₂ = (m / qB) 3v

 R₂ = 3 R

 R₂ / R = 3

The new radius is three times the initial radius