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

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, 21.7 cm, 505 turns, and 5.35 A. For the inner solenoid the corresponding quantities are 18.3 cm, 333 turns, and 1.85 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 5.55 mm?

And at what speed, v2, for an orbital radius of 15.7 mm?

Explanation / Answer

here,

for the outer solenoid

r1 = 0.02 m

length , l1 = 0.217 m

number of turns , n1 = 505

current , I1 = 5.35 A

for the inner solenoid

r2 = 0.01 m

length , l2 = 0.183 m

number of turns , n2 = 333

current , I2 = 1.85 A

net magnetic feild , B = u0 * n1 * I1 /l1 - u0 * n2 * I2 /l2

B = 1.26 * 10^-6 * ( 505 * 5.35 /0.217 - 333 * 1.85 /0.183)

B = 0.0114 T

for radius , R1 = 0.00555 m

let the speed be v1

R1 = m * v1 /( q * B)

0.00555 = 1.67 * 10^-27 * v1 /( 1.6 * 10^-19 * 0.0114)

v1 = 6061.8 m/s

for radius , R2 = 0.0157 m

let the speed be v2

R2 = m * v2 /( q * B)

0.0157 = 1.67 * 10^-27 * v2 /( 1.6 * 10^-19 * 0.0114)

v2 = 17147.8 m/s

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.