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, 20.9 cm, 593 turns, and 5.65 A. For the inner solenoid the corresponding quantities are 19.1 cm, 343 turns, and 1.37 A. At what speed, ????1, 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 5.53 mm?

Answer 1

9.03 x 10³ m /s

Step-by-step explanation:

magnetic field inside a solenoid

B = μ₀ n I , where μ₀ = 4π X 10⁻⁷ .

n is no of turns per unit length and I is current

so B₁ = 4π x10⁻⁷x 593 / 20.9 x 5.65 x 10²

201.5 x 10⁻⁴ T

B₂ = 4π x 10⁻⁷ x 343 / 19.1 x 1.37 x 10²

= 30.93 x 10⁻⁴ T

Net magnetc field

B₁ -B₂ = B = (201.5 - 30.93) x 10⁻⁴ T

B = 170.57 x 10⁻⁴ T

Now protons move in circular path of radius R in the magnetic field of B

B q v = m v² / R

v = B q R / m

= 170 .57 x 10⁻⁴ x 1.6 x 10⁻¹⁹ x 5.53 x 10⁻³ / (1.67 x 10⁻²⁷)

= 903.71 x 10

= 9.03 x 10³ m /s

=