Suppose that a parallel-plate capacitor has a circular plateswith a radius R - 3

Question

Suppose that a parallel-plate capacitor has a circular plateswith a radius R - 30mm and a plate seperation of 5mm. Susppose alsothat a sinusodial potential difference with a maximum value of 180Vand a frequency of 450 Hz is applied across the plates: thatis, V = ( 180 V ) sin [ 2 (450 Hz) t ] Find B max (R), the maximumvalue of the induced magnetic field that occurs at r=R. Suppose that a parallel-plate capacitor has a circular plateswith a radius R - 30mm and a plate seperation of 5mm. Susppose alsothat a sinusodial potential difference with a maximum value of 180Vand a frequency of 450 Hz is applied across the plates: thatis, V = ( 180 V ) sin [ 2 (450 Hz) t ] Find B max (R), the maximumvalue of the induced magnetic field that occurs at r=R.

Explanation / Answer

   we know that
   V = E d
   so that
   E = V / d
   using the equation from the theory we get
   B = (o o r /2) (dE / dt)
       = (oo r / 2 d) (dV / dt) for r < = R
   as the drivative of sin(t) = cos(t)
   so we get the magnetic field as a function of r as
   B = (o o r / 2d) Vmax cos(t)
   Bmax = (oo Vmax r / 2 d)
           =.......... T

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