An electron beam is making a circular orbit in a uniform magnetic field. The orb

Question

An electron beam is making a circular orbit in a uniform magnetic field. The orbit forms a closed circle.

(a) Choose all that are correct from the following.

The Lorentz force on the electrons is the centripetal force for the circular motion of the electrons.The Lorentz force on the electrons is in a direction perpendicular to the centripetal force for the circular motion of the electrons.     The electrons' circular orbit is in a plane parallel to the magnetic field.The Lorentz force is along the direction of the electrons' motion.

If the electrons are moving at a speed 5.950e+06 m/s and the magnetic field is 8.9 gauss, what is the radius of the electrons' circular orbit?
cm

Explanation / Answer

(a)   The correct option(s) from the given options:

  (i) The Lorentz force on the electrons is the centripetal force for the circular motion of the electrons.

(b)   As given in the question,

Magnetic field: B = 8.9 Gauss = 8.9*10^-4 T

Speed of electron: v = 5.95*10^6 m/s

Charge on electron: q = 1.6*10^-19 C

Mass of electron: m = 9.1*10^-31 kg

For the radius of the electrons' circular orbit,

Lorentz force:   F  = q*v*B

=> m*(v)^2 / R =   q*v*B

=> (9.1*10^-31)*(5.95*10^6)^2 / R  = (1.6*10^-19)*(5.95*10^6)*(8.9*10^-4)

=> R  = 0.038 m  = 3.8 cm

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