Question

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 3.64 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

Answer 1

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Step-by-step explanation:

Lorenz force exerted on electron by magnetic field is

F=e*v*H, where e=1.602E-19 C, H=3.64E-3 T, v is speed of electron;

? meanwhile Lorenz force is centripetal force F=m*v^2/r, where mass of electron m=9.11E-31 kg, r is radius of the path of electron;

? therefore F=F; e*v*H = m*v^2/r; eH=m*(v/r), hence

v/r = eH/m =w is angular speed of electron, hence

T=2pi/w =2pi*m/(eH) is period of rotation of electron;

e- and e+ starting at the same point are moving in the same circular path and in opposite directions, and should meet in T/2 time;

T/2 = pi*m/(eH) = pi*9.11E-31 /(1.602E-19 *3.48E-3) =5.13E-9 s;