How Do You Calculate the Specific Charge of an Electron Using Helmholtz Coils?

In summary, the conversation discusses the relationship between voltage and radius of deflection in Helmholtz coils, and how it can be used to calculate the specific charge of an electron. The equation for specific charge is (e/m) = 2V/(r^2 * B^2), where B represents the magnetic field. The accepted value of specific charge can be determined by using the accepted values for the charge and mass of an electron in the equation.
  • #1
aldrake
3
0
A constand current of 1A is flowing through the Helmholtz coils. When the voltage is altered the radius of the deflection beam changes accordingly. The trend line analysis of radius vs. voltage graphs give an equation of the form y=0.005x+25. (Hint: graph is plotted by considering r^2 (m^2) on y-axis and V(volts) on x-axis.)

a) calculate the specific charge of an electron

b) How do you determine the accepted/standard value of specific charge? (Show your calculations)



(e/m) = 2V/(r^2 * B^2)

I know how to calculate the magnetic field, B, based on a different given formula.

I think I'm making this more difficult than it has to be. Could someone please explain where I need to start with this. Can I replace V/r^2 with the given slope of 0.005?
 
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  • #2
r² on the vertical axis and V on the horizontal suggests slope = r²/V
 
  • #3
Okay. Can I substitute the inverse of the slope 1/(0.005) into the equation (e/m)=2V/(r^2 *B^2). Doing this I get (e/m)= 400/(B^2). I can calculate B^2 and solve. Does this seem reasonable?
 
  • #4
Looks good!
 
  • #5
Can you determine the standard value of specific charge by simply using the accepted values for the charge of an electron and the accepted values for the mass of an electron (e/m)?
 
  • #6
Yes, do check the answer that way. It should be reasonably close to the expected value.
 

FAQ: How Do You Calculate the Specific Charge of an Electron Using Helmholtz Coils?

What is the specific charge of an electron?

The specific charge of an electron is the ratio of its charge to its mass. It is represented by the symbol "e/m" and has a constant value of -1.76 x 10^11 coulombs per kilogram (C/kg).

How was the specific charge of an electron first determined?

The specific charge of an electron was first determined by J. J. Thomson in his famous cathode ray tube experiment in 1897. He measured the deflection of the electron beam in the presence of an electric and magnetic field to calculate the ratio of e/m.

Why is the specific charge of an electron important?

The specific charge of an electron is an important physical constant that helps us understand the fundamental properties of matter. It also plays a crucial role in various applications such as particle accelerators, mass spectrometry, and nuclear medicine.

Does the specific charge of an electron change?

No, the specific charge of an electron is a constant value and does not change. This means that the charge and mass of an electron are directly proportional to each other, and any change in one will result in a corresponding change in the other.

How does the specific charge of an electron relate to other subatomic particles?

The specific charge of an electron is much higher than that of a proton or neutron, meaning that it has a stronger charge-to-mass ratio. This is one of the reasons why electrons are used in many technological applications, such as electricity and electronics.

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