Answer:
The new radius is three times the initial radius
Step-by-step 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