Plated Magnetic

Plated Magnetic

How does the magnetic field vary with time in a capacitor?

A capacitor of capacitance C is in a vacuum, and has a charge Q0, plate radius a and separation d.
At t = 0, it is connected to a resistor of resistance R and discharges.
The charge on the plates is given by:
Q(t) = Q0 * e^(-t/?) where ? = R * C.

The voltage on the capacitor is Q/C. The field in the capacitor is Q/(C*d). The field is therefore

E(t) = Q0 * e^(-t/?) /(C*d)

The magnetic field is given by ?B*dL = µ0*?0*?/?t ?E*dA.

Because of the uniformity of the fields, the integrals can be simplified:

at a distance r from the center, ?B*dL = B*2*?*r and ?E*dA = E*?*r²

B*2*?*r = µ0*?0*?*r²*?/?t E(t)

B =0.5* µ0*?0*r*?/?t E(t)

?/?t E(t) = -(1/?)*Q0 * e^(-t/?) /(C*d)

B = -0.5* µ0*?0*r*(1/?)*Q0 * e^(-t/?) /(C*d)

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MAYFIELD HEIGHTS, Ohio----Brush Engineered Materials Inc. announced today that the Company, through its wholly-owned subsidiary, Williams Advanced Materials Inc. , has completed the earlier announced acquisition of Academy Corporation.

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