Two solenolds are nested coaxially such that their magnetic fields point in oppo

Question

Two solenolds are nested coaxially such that their magnetic fields point in opposite directions. Treat the solenolds 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, 505 turns, and 5.83 A. For the inner solenoid the corresponding quantities are 18.5 cm. 395 turns, and 1.31 A. At what speed, v_1 should a proton be traveling, Inside the apparatus and perpendicular to the magnetic field. If is is to orbit the axis of the solenoids at a radius of 5.97 mm? v_1 And at what speed, v_2. for an orbital radius of 13.9 mm? v_2 =

Explanation / Answer

Part a) B = B1 + B2

B = u0 N1 i1/L1 - u0 N2 i2/L2

B = 4*3.1416e-7*595*5.83/0.219 - 4*3.1416e-7*395*1.31/0.185 = 0.016381343 T

v_1 = R q B/m = 5.97e-3*1.6e-19*0.016381343/1.67e-27 = 9369.7358 m/s =====PART A )

Part b)

B = u0 N1 i1/L1

B = 4*3.1416e-7*595*5.83/0.219 = 0.019894409 T

v_1 = R q B/m = 13.9e-3*1.6e-19*0.019894409 T/1.67e-27 = 26494.11132 m/s =======ANSWER) PART B )

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