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An electron enters one end of a solenoid with a speed of 800 m/s, making an angle of 30 degrees with the central axis of the solenoid. The solenoid carries a current of 4.0 A and has 8000 turns along its entire length. How many complete revolutions does the electron make inside the solenoid before emerging from the other end? (Use charge-to-mass ratio e/m = sqrt(3) x 10¹¹ C/kg.) Express the answer as 5 x 10^y and find y.
- y = 3
- y = 4
- y = 5
- y = 6
Correct answer: y = 4
Solution
The magnetic field inside the solenoid is B = mu0 * n * I. The electron's velocity component along the axis gives the pitch, and the perpendicular component gives the circular motion. The number of revolutions equals the axial transit time divided by the cyclotron period.
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