A particular type of fundamental particle decays by transfor

A particular type of fundamental particle decays by transforming into an electron e^- and a positron e^+. Suppose the decaying particle is at rest in a uniform magnetic field B of magnitude 3.97 mT and the e^- and e^+ move away from the decay point in the paths lying in a plane perpendicular to B. How long after the decay do the e^- and e^+ collide?

Solution

Suppose e- and e+ moves with velocity v.

then magnetic force will be, Fb = q ( v x B)

Fb will be perpendicular to the v and both particle will travel in circular path.

and magnitude of Fb will be same for both.

Fb = q v B = m v^2 / r

v / r = q B / m

both particle will meet after traveling half cirle.

so time will be = pi r / v = pi ( r / v )

and r / v = m / q B

t = pi ( m / q B) = pi ( 9.109 x 10^-31 / (1.6 x 10^-19x 3.97 x 10^-3))

t = 4.505 x 10^-9 sec