Use Maxwell\'s extension of Ampere\'s Law to obtain a relation as a function of

Question

Use Maxwell's extension of Ampere's Law to obtain a relation as a function of both position and time for the magnetic field between the plates of a vacuum-filled capacitor as it is being charged in an RC circuit. Assume circular plates of radius R_plate,. and separation d_plate, a power supply that provides a potential difference C, and the resistance in the circuit is The capacitor begins with no charge and the switch is closed at t = 0. Your solution will include only the quantities mentioned above (so no variables for current should remain), physical constants, math constants like 71, and the variables t and r. Show explicitly that the units in your final expression work (that is, it eventually all turns into tesla), Evaluate your expression for 1220V, R_resist = 50 Ohm, R_plate = 0.05m, and d = 1.00 Times 10^-3 m.

Explanation / Answer

Here,   V = Ed

=>    I * (Rresist + Rplate) = (E + uodB/dt) * dplate

=>    I * (50 + Rplate) = (E + uodB/dt) * 10-3

=>   E =   1452.45 N/C

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