The electric flux through any closed surface is equal to the electric chargeĮnclosed by the surface. The current into the capacitor after the circuit is closed, is therefore Then the z-component of the electric field between the plates as a function of time axis point from the positive plate to the negative plate.
We can use the equations from the analysis of anĬircuit ( Alternating-Current Circuits) plus Maxwell’s version of Ampère’s law.Ī. (b) From the properties of the capacitor, find the corresponding real currentĪnd compare the answer to the expected current in the wires of the corresponding (a) Find the displacement current between the capacitor plates at time Where the contribution comes from the actual flow of electric charge.ĭisplacement current in a charging capacitorĪ parallel-plate capacitor with capacitance Where the right-hand side results from the displacement current, as it is for the surface Thus, the modified Ampère’s law equation is the same using surface In Equation 13.1.5 with the closed Gaussian surface Therefore, we can replace the integral over Gauss’s law for electric charge requires a closed surface and cannot ordinarily be applied to a surface likeįorm a closed surface in Figure 13.1.2 and can be used in Gauss’s law. Through which no actual current flows, the displacement current leads to the same valueįor the right side of the Ampère’s law equation. Therefore, theįield and the displacement current through the surfaceĪre both zero, and Equation 13.1.2 takes the form In Equation 13.1.3 is between the capacitor plates. Is measured.We can now examine this modified version of Ampère’s law to confirm that it holds independent of whether the surface When this extra term is included, the modified Ampère’s law equation becomes It accounts for a changing electric field producing a magnetic field, just as a real current does, but the displacement current can produce a magnetic field even where no real current is present. It is produced, however, by a changing electric field. The displacement current is analogous to a real current in Ampère’s law, entering into Ampère’s law in the same way. Where the displacement current is defined to be How can Ampère’s law be modified so that it works in all situations? Maxwell suggested including an additional contribution, called the displacement current This may not be surprising, because Ampère’s law as applied in earlier chapters required a steady current, whereas the current in this experiment is changing with time and is not steady at all.
Gives zero for the enclosed current because no current passes through it:Ĭlearly, Ampère’s law in its usual form does not work here. Gives a nonzero value for the enclosed current Shown at a time before the capacitor is fully charged, so that A source of emf is abruptly connected across a parallel-plate capacitor so that a time-dependent currentĭevelops in the wire.
There are infinitely many surfaces that can be attached to any loop, and Ampère’s law stated in Equation 13.1.1 is independent of the choice of surface.Ĭonsider the set-up in Figure 13.1.2. Passing through any surface whose boundary is loop Recall that according to Ampère’s law, the integral of the magnetic field around a closed loop Maxwell discovered logical inconsistencies in these earlier results and identified the incompleteness of Ampère’s law as their cause. The four basic laws of electricity and magnetism had been discovered experimentally through the work of physicists such as Oersted, Coulomb, Gauss, and Faraday.