Question

A solenoid with 25 turns per centimeter carries a current II. An electron moves within the solenoid in a circle that has a radius of 2.0 cm and is perpendicular to the axis of the solenoid. If the speed of the electron is 2.0\times 10^5~\text{m/s}2.0×10 ​5 ​​ m/s, determine what the current in the solenoid windings must be.

Answer 1

Answer: The current in the solenoid windings must be 0.0181A

Explanation: Please see the attachments below

Answer 2

Answer:

Current = 0.0181 A

Explanation:

Radius, R = 2.0 cm = 0.02 m

Speed of the electron, v = 2 * 10⁵ m/s

Mass of an electron, M = 9.109 * 10⁻³¹kg

Charge of an electron, q = 1.602 * 10⁻¹⁹C

Current in the solenoid, I = ?

Centripetal force, F = Mv²/R

$F = \frac{9.109 * 10^{-31}*(2*10^{5} )^{2} }{0.02} \\F = 182.18 * 10^{-20} N$

Magnetic force in the solenoid

F = qVB

182.18 * 10⁻²⁰ = 1.602 * 10⁻¹⁹ * 2 * 10⁵ * B

B = (182.18 * 10⁻²⁰)/(3.204 * 10⁻¹⁴)

B = 56.86 * 10⁻⁶T

B = 56.86 μT

N = 25 turns/cm = 25 * 100 = 2500 turns/m

To get the value of the current in the solenoid winding

$B = N \mu_{o} I\\56.86 * 10^{-6} = 2500*4\pi * 10^{-7} I\\I = (56.86 * 10^{-6})/(2500 *4\pi * 10^{-7} )\\I = 0.0181 A$