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, 20.3 cm, 553 turns, and 4.17 A. For the inner solenoid the corresponding quantities are 19.3 cm, 383 turns, and 1.35 A.

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 6.83 mm?

And at what speed, v2, for an orbital radius of 14.9 mm?

Answer 1

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, 21.3 cm, 577 turns, and 4.65 A. For the inner solenoid the corresponding quantities are 18.5 cm, 335 turns, and 1.19 A. 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 5.51 mm? v1=_____ m/s And at what speed, v2, for an orbital radius of 17.7 mm? v2=_____m/s

case of ideal solenoids B =UoN1I1/L1 -UoN2I2/L2 B= 4*pi*10^(-7) ( 577*4.65/.185- 335*1.19/.213) B= 0.0158 T centripetral force for circular motion provided by magnetic field so q*v1*B=m*v1^(2)/R v1=q*B*r/m V1= 163096 m/s 2nd part field due to inner solenoid will be zero because point lies outside of it so B=UoN1I1/L1 v2=q*B*r/m and solve it.