An electron moving with velocity v = 2 times 10 m/s moves into a uniform magneti

Question

An electron moving with velocity v = 2 times 10 m/s moves into a uniform magnetic field directed out of the page of strength B = 30 T as shown below. Determine the direction of the force on the electron as it enters the magnetic field Determine the magnitude of the force on the electron as it enters the magnetic field Describe the subsequent motion of the electron, (what type of path does it follow and why). Calculate the radius of the electron's orbit in the field Suppose the electron had entered the field at an angle other than perpendicular to the field direction. Describe the subsequent motion.

Explanation / Answer

a. F = q(v X B) B is in z direction, v is in x direction. so, v X B will be in -y direction. But since q of electron will be negative, F will be in positive y direction. b. F = 1.6*10^-19 * 2*10^6 * 30 = 9.6*10^-12 N c. The force will always be perpendicular to the motion of electron and so it moves in circular path. d. F = mv^2 /r 9.6*10^-12 = 9.1*10^-31 * 4*10^12/r r = 3.79*10^-7 m e. electron will move in spiral motion.

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