Question

What is the velocity of a beam of electrons that goes undeflected when moving perpendicular to an and to a magnetic field E and B are also perpendicular to each other and have magnitudes 7.7 times 10^3 V/m and 7.5 times 10^-3 T, respectively. What is the radius of the electron orbit if the electric filed is turned off?

Answer 1

(a) If electron move undeflected then the force due to the electric and magnetic field should cancel each other.
Hence
qE = qVB
where E is electric field , V is velocity of beam , q is charge and B is the magnetic field
V = E/B = 7.7*10³ / 7.5*10^-3 = 1.0267*10⁶ m/s
(b) when the electric field is turned off then electron will follow the ciruclar path and
centripetal force will be provided by the magentic field , hence
mv² /r = qvB
r = mv/qB = ( 9.11*10^-31*1.027*10⁶) / (1.6*10^-19*7.5*10^-3) = 7.797*10^-4 m