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I understand how the displacement current work in dielectric such as in parallel plate capacitors but don't know how they would work in a vacuum where there is no dielectric present. Can someone please explain.

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The displacement current only refers to the current flowing in the wires of the capacitor when it is being charged or discharged. Since the charges cannot jump from one plate to the other, the charges are instead displaced, building up on one plate and depleting the other, hence the term 'displacement current'. This charge displacement results in an increasing electric field in the direction of the current flow. The increasing electric field generates a circulating magnetic field that would have the same magnitude as if there was actually a current carrying wire there. Since electric and magnetic fields can be present in free space, this effect can be seen in a vacuum.

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