Acharge 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?

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

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