You have arranged that the magnetic field in a particular region of space is due

Question

You have arranged that the magnetic field in a particular region of space is due North with a value of 0.0090 T. An electron enters the field traveling to the West with a speed of 7.5 percent of the speed of light. As a result, the electron experiences a magnetic force which is upwards. (a) What is the strength of this magnetic force? Give your answer in femtonewtons. fN (b) What is the amount of the resulting acceleration of the electron? Get the mass of an electron from the inside back cover of your textbook. Give your answer in Pm/s^2 Pm/s^2 (c) What will be the result of the acceleration that you have calculated in part (b)? The speed of the moving electron will change but its direction of motion will remain constant.. The direction of the moving electron will change but its speed will remain constant. Both the speed and direction of the moving electron will change.

Explanation / Answer

velocity v = (7.5/100) x 3 x 108 = 22500000 m/s

a.) the magnitude of the Magnetic force on a moving charge is given by F = qvB when velocity and the magnetic field are perpendicular as in our case

F = e v B = 1.60217662 × 10-19 x 22500000 x 0.0090 = 3.244407656 x 10-14 N = 32.44 x 10-15 N

F = 32.44 fN

b.) mass of electron me  = 9.10938356 × 10-31 kg

acceleration a = F/me = 3.244407656 x 10-14 / 9.10938356 × 10-31 = 3.561610546 x 1016 m/s2 = 35.6 Pm/s2

c.) The magnetic force is always acting perendicular to the direction of velocity and hence does no work. So the speed will not change. But the direction sure changes. The electron actually moves in a vertical circle. where its direction changes continously but not the speed.

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