Maxwell's Equations: B-field induced from changing E-field

[Bryon]

Homework Statement

Parallel plate capacitor with circular plates with radius of 26mm and a plate separation of 6mm. A sinusiodal potential difference is applied across the capacitors plates with Vmax = 170V at a frequency of 60Hz.

170sin(2*pi*60Hz*t)

Homework Equations

V = ∫E∙dl = El (l is the distance)

Maxwell-Ampere
∫B∙dl = u0(I + ε0(dΦe/dt))

A = pi*r^2

dΦ^e/dt = dEA/dt = A(dE/dt)

The Attempt at a Solution

B2*pi*r = u₀ *ε₀*A(dE/dt)

E = 170sin(2*pi*60Hz*t)/(0.003)V/M (I used the distance between the plates to find the e-field).

dE/dt 170sin(2*pi*60Hz) = 20400*pi*cos(120*pi*t)/(0.003)

∫B∙dl = B*2*pi*r

B*2*pi*0.013 = u₀ *ε₀*(pi*0.026^2)* 20400*pi*cos(120*pi*t)/(0.003)

B = 6.17711x10^-12 T

I thought I was on the right track, but it turns out that this was not correct. I think this was my best approach to the problem and at this point I do not know what else to try. I have a feeling that the electric field is not correct but I do not see what is wrong with it. Any suggestions?

 

[Bryon]

Anyone? I know, its a toughy, but I figured a second pair of eyes could point me in the right direction.

 

[Bryon]

Wow, no one. Well, at least I am not alone! lol

 

[khemist]

You didnt state what you are solving for. I am assuming the maximum strength of the b field?

 

[Bryon]

Thanks! I was forgetting something. lol. I also noticed I made another error when I copied it over from my work...Yeah, I'm frustrated with this one and all the others problems that are asking about the magnetic field.

(a) What is amplitude of the induced magnetic field a distance 13 mm from the center axis joining the plates?

B2*pi*r = u0 *ε0*A(dE/dt)

E = 170sin(2*pi*60Hz*t)/(0.003)V/M (I used the distance between the plates to find the e-field).

dE/dt 170sin(2*pi*60Hz) = 20400*pi*cos(120*pi*t)/(0.006) <---should be 6mm instead of the 3mm
∫B∙dl = B*2*pi*r

B*2*pi*0.013 = u0 *ε0*(pi*0.026^2)* 20400*pi*cos(120*pi*t)/(0.006)

B = 9.83117439x10^-13 T