Mass of an Electron: Helmholtz Coil Relation

In summary, the conversation discusses the use of Helmholtz coils to determine the relationship between magnetic force and mass, leading to the calculation of the mass of the electron. The equations used include F = Bev, Bev = mV^2 / r, and ½mv^2 = eV. The final equation for calculating the mass is m = 3.09 x 10^-27 I^2r^2 / V, with the constant e/k = 1.602 x 10^-19/ 5.18 x 10^7 = 3.09 x 10^-27. The conversation concludes with a request for a specific question to address any confusion.
  • #1
greze9
2
0

Homework Statement



Using Helmholtz coils we found the relationship between magnetic force and mass and therefore coming up with the mass of the electron, but I am so confused on how the process actually works in relation to the strength of the current in proportion to the strength of voltage.

Homework Equations



F = Bev
Bev = mV^2 / r
½mv^2 = eV
e/m = 2V / B^2r^2
B = 8μ0N x I
√125 a
e/m = (1.95/ μ0 x a^2/N^2) 2V/ I^2r^2 =(5.18 x 10^7) V/ I^2r^2; or, in simpler terms:
e/m = K x V/ I^2r^2
: m = e/k x I^2r^2 / V
e/k = 1.602 x 10-19/ 5.18 x 107 = 3.09 x 10^-27. Therefore, m = 3.09 x 10^-27 I^2r^2 / V.

these are the equations we ended up producing and therefore using...

The Attempt at a Solution

 
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  • #2
We're going to need a question. It's very tedious to try to give a full lecture through this medium. Try to be more specific as to where you get confused.

For starters, do you know what the first three equations your list "say"?
 
  • #3


I can understand your confusion about the process and equations involved in determining the mass of an electron using Helmholtz coils. Allow me to provide some explanation and clarification.

Firstly, Helmholtz coils are a type of electromagnet consisting of two identical coils with the same radius, placed parallel to each other and separated by a distance equal to their radius. This configuration creates a uniform magnetic field in the space between the coils, which is essential for this experiment.

In order to determine the mass of an electron, we use the relationship between magnetic force (F) and mass (m) in the equation F = Bev, where B is the strength of the magnetic field, v is the velocity of the electron, and e is the charge of the electron.

Next, we use the equation Bev = mV^2 / r, which relates the magnetic force to the centripetal force experienced by the electron as it moves in a circular path of radius r. This equation can be rearranged to ½mv^2 = eV, where V is the voltage applied to the coils.

We then use the equation e/m = 2V / B^2r^2, which relates the charge-to-mass ratio of the electron to the voltage and the strength of the magnetic field. This equation can be simplified to e/m = K x V/ I^2r^2, where K is a constant derived from other fundamental constants.

Finally, by measuring the voltage (V), current (I), and radius (r) of the coils, we can calculate the mass of an electron using the equation m = e/K x I^2r^2 / V.

In summary, the process involves using the magnetic force and centripetal force equations, along with the known values of voltage, current, and coil radius, to determine the mass of an electron. I hope this explanation helps to clarify the process for you.
 

What is the relationship between the mass of an electron and Helmholtz coils?

According to the Helmholtz coil relation, the mass of an electron is determined by the strength of the magnetic field produced by the Helmholtz coils.

How is the mass of an electron measured using Helmholtz coils?

The mass of an electron can be measured by observing the radius of the electron's circular motion within the magnetic field created by the Helmholtz coils. The stronger the magnetic field, the smaller the radius and thus, the greater the mass of the electron.

What other factors can affect the accuracy of the mass of an electron measurement using Helmholtz coils?

Other factors that can affect the accuracy of the measurement include the precision of the Helmholtz coils' dimensions and the stability of the power supply and current used to create the magnetic field.

How does the Helmholtz coil relation contribute to the understanding of the electron's mass?

The Helmholtz coil relation provides a quantitative relationship between the magnetic field and the mass of an electron. This allows for a more precise and accurate measurement of the electron's mass, leading to a better understanding of its properties.

Are there any limitations to the Helmholtz coil relation for measuring the mass of an electron?

While the Helmholtz coil relation is a useful tool for measuring the electron's mass, it assumes a circular motion of the electron within the magnetic field. In reality, the electron's motion may not be perfectly circular, leading to slight discrepancies in the measured mass. Additionally, the mass of an electron can also be affected by external factors such as temperature and pressure, which may not be accounted for in the Helmholtz coil relation.

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