An electron is created in a cathode ray tube. It is first accelerated from the C

Question

An electron is created in a cathode ray tube. It is first accelerated from the Cathode (from rest) to the Anode with a potential difference of 600V. A hole in the anode allows the electrons to travel straight through. What is the speed of these electrons? Let's say we change the voltage so that the speed of the electrons is 1.0 Times x 10^7 m/s. Recalling that the magnetic force is a centripetal force, what radius circle will these electrons move in if a magnetic field of 0.01 T is applied (with no electric field)? What electric field is required to cancel this deflection?

Explanation / Answer

(a.) Potential energy = qV = 1.6*10-19 *600

Potential energy will be get converted into kinetic energy

1/2 MeV2 = 1.6*10-19 *600

0.5*9.1*10-31V2 = 1.6*10-19 *600

V = 18.02*106 m/s

(b.) V = 1.0*107 m/s

B = 0.01 T

r = mV/qB = (9.1*10-31*107 ) /(1.6*10-19*0.01) = 5.69*10-3 m = 5.69 mm

(c.) qE = q(VB)

E = 107 * 0.01 = 105 N/C

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