A stream of electrons travelling with speed of v m/s at right angles to a uniform electric field E is - Physics - Electric Charges And Fields

Question

A stream of electrons travelling with speed of v m/s at right
angles to a uniform electric field E is deflected in a circular
path of radius r Prove that e/m =v2 /rE ?

Neha Sarin · Accepted Answer

We know that the path of the particles in
transverse electric field is parabola

Here the path of electron is given as a
circle; we may assume a small arc of parabola as circular arc of
radius r , the necessary centripetal force [
mv2/r] for a circular arc is provided by the
electric force (eE) so we have

mv2/r = (eE)

e/m = v2 /rE

A stream of electrons travelling with speed of v m/s at right angles to a uniform electric field E is deflected in a circular path of radius r.Prove that e/m =v2 /rE ?