Question

Two solenoids are nested coaxially such that their magnetic fields point in opposite directions. Treat the solenoids as ideal. The outer one has a radius of 20 mm, and the radius of the inner solenoid is 10 mm. The length, number of turns, and current of the outer solenoid are, respectively, 21.9 cm, 519 turns, and 4.15 A. For the inner solenoid the corresponding quantities are 18.7 cm, 391 turns, and 1.35 A. The elementary charge is 1.602×10−19 C, the mass of the proton is 1.673×10−27 kg, and the vacuum permeability constant has the value 4π×10−7 T⋅m/A.

1. At what speed v1 should a proton be traveling, inside the apparatus and perpendicular to the magnetic field, if it is to orbit the axis of the solenoids at a radius of 6.61 mm?

2. At what speed v2 should a proton be traveling if it is to orbit the axis of the solenoids at a radius of 15.7 mm?

Answer 1