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30.14: Ampere-Maxwell's Law: Problem-Solving

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Ampere-Maxwell's Law: Problem-Solving

30.14: Ampere-Maxwell's Law: Problem-Solving

A parallel-plate capacitor with capacitance C, whose plates have area A and separation distance d, is connected to a resistor R and a battery of voltage V. The current starts to flow at t = 0. What is the displacement current between the capacitor plates at time t? From the properties of the capacitor, what is the corresponding real current?

To solve the problem, we can use the equations from the analysis of an RC circuit and Maxwell's version of Ampère's law.

For the first part of the problem, the voltage between the plates at time t is given by


Suppose that the z-axis points from the positive plate to the negative plate. In this case, the z-component of the electric field between the plates as a function of time t is given by


Therefore, the z-component of the displacement current Id between the plates of the capacitor can be evaluated as


where the capacitance Equation 4 is being used.

Further, to solve the second part of the above-stated problem, the current into the capacitor after the circuit is closed can be obtained by the charge on the capacitor, which in turn can be evaluated by using the expression for VC. As a result, the real current into the capacitor is found to be the same as the displacement current.

Suggested Reading


Ampere-Maxwell's Law Problem-solving Parallel-plate Capacitor Capacitance Plates Area Separation Distance Resistor Battery Voltage Current Flow Displacement Current Real Current RC Circuit Analysis Maxwell's Version Of Ampère's Law Voltage Between Plates Z-component Of Electric Field Evaluation Of Displacement Current Charge On Capacitor Expression For VC Real Current Into Capacitor

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