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.

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

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

the one with the highest speed

kepler used the data from tycho blahe (his mentor) to construct the laws of planetary motion.