Asolenoid with 33 turns per centimeter carries a current i. an electron moves within the solenoid in a circle that has a radius of 2.1 cm and is perpendicular to the axis of the solenoid. if the speed of the electron is 3.6 ✕ 105 m/s, what is i (in a)?

To develop this problem it is necessary to match the concepts related to electromagnetic force and the centripetal Force.

By definition we have that the centripetal Force is equivalent to

Where,

m = Mass (of a electron)

v = Velocity

R = Radius

At the same time we have that magnetic force is equal to

Where,

q = Charge

V = Velocity

B = Magnetic Field

Equating both we have,

Re-arrange to find B,

Replacing with our values we have,

Now for Faraday's law the Magnetic field in a solenoid is defined as,

Re-arrange to find I

Where,

B = Magnetic Field

Permeability constant

N = Number of loops per meter

Replacing with our values

Therefore the Current is 0.235115A

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