A charged particle q’ is moving with a speed V perpendicular to the magnetic field of induction B. Find the radius of the path and the time period of the particle.

# A charged particle q' is moving with a speed V

**prasanna**#2

Let us assume that the field is directed into the page as shown in figure. Then the force experienced by the particle is F = qvB. We know that this force is always directed perpendicular to velocity. Hence the particle moves along a circular path and the magnetic force on a charged particle acts like a centripetal force.

Let r be the radius of the circular path.

We know that centripetal force = m${{v}^{2}}$ / r

q v B = m${{v}^{2}}$ / r

Solving this equation, we get; r = mv / Bq

Time period of the particle; T = 2$\pi$r / v

Substituting r in above equation, we get

T = 2$\pi$m / Bq