1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Find a relationship between C & E

  1. Jul 19, 2008 #1
    1. The problem statement, all variables and given/known data
    Given a coaxial cylindrical capacitor with a dialectric constant of 87.9, what field strength is needed to oscillate a dipole within the field at 175,000 hz...?

    What dimensions would the capacitor have in order to produce the field strength needed for that oscillation...?



    2. Relevant equations

    Given that Torque = P (dipole moment) X E(field strength)

    T= P X E

    & T=I (moment of Inertia) * a (alpha, angular accelleration)

    Therefore P X E = I * a

    rearranging a = P X E/I

    For simple harmonic motion, T (period in seconds) = 2*pi*sqrt(I/P X E)

    T= 1/f

    P= 6.24E-30 C m

    I = (z axis) = 1.92E-47 Kg m^2


    3. The attempt at a solution

    My result yields the E (field strength) of 2.67E5 N/C

    If this is correct, what capacitor design will provide this given the following constraints?

    Radius no greater than approximately 7 cm for the outer electrode

    Electrode length no longer than approximately 30 cm for both electrodes

    What voltage will be applied?
     
  2. jcsd
  3. Jul 20, 2008 #2
    I did come up with something else....

    Taking the Capacitance of charged coaxial cylinders to be 2*Pi* (Epsilon Naut) * L (length of the capacitor) ? ln(b/a), where

    Epsilon Naut= 8.85E-12

    L = .1 meters

    b= radius of outer electrode = 3.81 cm

    and a = radius of inner electrode = 1.91 cm

    I found that C = 8.08E-12 N/C

    Multiplied by the dielectric constant 87.9 gave me 6.474E-10

    Then I set Q = C*V where V= 12 Volts, giving me a total charge of 7.77E-9 C

    After that, I used Guassian symmetry to determine the radius of the field from one electrode to the field strength of 5.87E5 N/C

    E = Q/L*2*Pi*Epsilon Naut*r

    rearranging gives Q/E*L*2*Pi*Epsilon Naut = radius

    Thus the distance from the cylinder to a point where the field strength (E) is 5.23 mm. At this point, a dipole at the forementioned moment for both interia and dipole will oscillate at a frequency of 175,000 hz.

    Unless my Field Strength is incorrect from the first problem. Which is possible because my physics professor included a "2" to be multiplied with P & E in the first equation.

    Does anyone know if this is correct???

    Thanks for your help!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?