Electric Current of an Orbiting Electron

In summary, the question involves finding the value of k in the equation I = e2 / sqrt(k*ε0*r3*m), which is based on the Bohr model with an electron and a proton. Using Coulomb's force law and the centripetal force, the equation mω2r = ke2/r2 is derived. After rearranging and substituting for ω, the equation 2π/T = ke2/mr3 is obtained. From here, the use of current (I = q/t) is suggested to solve for k.
  • #1
FelaKuti
19
0

Homework Statement


The question is based on the Bohr model with an electron with charge e and mass m orbiting a proton about a circular radius r.

I have to find k in the equation I = e2 / sqrt kε0r3m

where k is a some combination of constants.

Homework Equations



Coulumb's force law: F = kq1q2/r2

Centripetal force: mω2r

Current: I = q/t

k = 1/4πε0

The Attempt at a Solution



I equated columb's force law to the centripetal force to give mω2r = ke2/r2

Then rearranged to get ω2 = ke2/mr3

Then I changed ω for 2π/T and square rooted both sides to give 2π/T = ke2/mr3

From here I'm just not sure how to get it into the form of the equation asked for.
 
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  • #2
FelaKuti said:
ω2 = ke2/mr3

2π/T = ke2/mr3
The left side of the second equation above has an error (maybe just typographical).

From here I'm just not sure how to get it into the form of the equation asked for.
Try to make use of I = q/t.
 

FAQ: Electric Current of an Orbiting Electron

1. What is an electric current?

An electric current is the flow of electric charge through a conductor or medium. It is typically measured in amperes (A) and is caused by the movement of charged particles, such as electrons.

2. How does an electron's orbit affect electric current?

An electron's orbit determines its speed and direction of movement, which in turn affects the flow of electric charge and creates an electric current. The faster an electron moves and the more it deviates from a straight path, the stronger the current will be.

3. Can an electron's orbit change the direction of an electric current?

Yes, an electron's orbit can change the direction of an electric current. This is because the direction of an electric current is determined by the movement of negatively charged particles, such as electrons. If the electron's orbit changes, the direction of its movement and the flow of electric charge will also change, resulting in a change in the direction of the current.

4. How does the shape of an electron's orbit affect electric current?

The shape of an electron's orbit can affect the strength and direction of an electric current. For example, a circular orbit will result in a constant current, while an elliptical orbit will cause the current to vary in strength as the electron moves closer or further away from the nucleus. Additionally, a tilted orbit can also change the direction of the current.

5. What factors can influence an electron's orbit and, therefore, electric current?

Several factors can influence an electron's orbit and, consequently, the flow of electric current. These include the strength and direction of an external magnetic field, the electric potential of the surrounding environment, and the presence of other charged particles that may interact with the electron's path.

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