Solenoid Equation Help: Finding Current with Electron Motion

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In summary, the problem is asking for the current i in a long solenoid, given that an electron is moving in a circular path within the solenoid with a specific speed and radius. The formula for the magnetic field of the solenoid without the electron is given, and the next step is to calculate the magnetic field of the circular loop created by the moving electron. The idea is to equate the two magnetic fields and solve for i.
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KoGs
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Homework Statement


A long solenoid has 100 turns/cm and carries current i. An electron moves within the solenoid in a circle of radius 2.30 cm perpendicular to the solenoid axis. The speed of the electron is 0.04640c (c= speed of light). Find the current i in the solenoid



B = permeability constant * i * 100turns/cm for the solenoid without the electron.


I guess I need the speed of the electron somewhere.

F = ma
qvB = m (v^2)/r
So we can get B of the circular loop.

What do I do next? I don't suppose we just equate these two B's.
 
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  • #2
KoGs said:

Homework Statement


A long solenoid has 100 turns/cm and carries current i. An electron moves within the solenoid in a circle of radius 2.30 cm perpendicular to the solenoid axis. The speed of the electron is 0.04640c (c= speed of light). Find the current i in the solenoid



B = permeability constant * i * 100turns/cm for the solenoid without the electron.


I guess I need the speed of the electron somewhere.

F = ma
qvB = m (v^2)/r
So we can get B of the circular loop.

What do I do next? I don't suppose we just equate these two B's.

There's an idea. The only thing around producing a field to bend the path of that electron is the solenoid.
 

Related to Solenoid Equation Help: Finding Current with Electron Motion

1. What is the solenoid equation?

The solenoid equation, also known as the Biot-Savart law, is a mathematical expression that describes the magnetic field produced by a current-carrying wire or solenoid. It states that the magnetic field at a point is directly proportional to the current, length, and number of turns of the wire, and inversely proportional to the distance from the wire.

2. How is the solenoid equation used?

The solenoid equation is used in many applications involving electromagnets, such as in motors, generators, and MRI machines. It allows scientists and engineers to calculate the magnetic field strength at a specific point, which is essential for designing and optimizing these devices.

3. What are the units of the solenoid equation?

The units of the solenoid equation depend on the system of measurement being used. In the SI system, the units are Tesla (T) for magnetic field, Ampere (A) for current, and meter (m) for distance. In the CGS system, the units are Gauss (G) for magnetic field, Ampere (A) for current, and centimeter (cm) for distance.

4. How does the solenoid equation differ from the magnetic field equation for a straight wire?

The solenoid equation describes the magnetic field produced by a coiled wire, while the magnetic field equation for a straight wire is used for a single, straight wire. The solenoid equation takes into account factors such as the number of turns and length of the wire, while the straight wire equation does not.

5. What are some real-life applications of the solenoid equation?

The solenoid equation is used in various technologies, such as electric motors, speakers, and computer hard drives. It is also used in medical devices like MRI machines and in research experiments involving electromagnets. Additionally, the solenoid equation is used in everyday household items, such as doorbells and electric locks.

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