# Find a relationship between C & E

1. Jul 19, 2008

### seekingaeolus

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. Jul 20, 2008

### seekingaeolus

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???