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

[aldrake]

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?

 

[Delphi51]

r² on the vertical axis and V on the horizontal suggests slope = r²/V

 

[aldrake]

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?

 

[Delphi51]

Looks good!

 

[aldrake]

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)?

 

[Delphi51]

Yes, do check the answer that way. It should be reasonably close to the expected value.