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I came across a line stating that a magnetic field exists in a region outside a circular plate capacitor that is being charged. I am not able to understand this as there is no change in electric flux and according to Maxwell's law of induction, magnetic field can't be induced without a change in electric flux. I've attached photos of the diagram and the statements (enclosed within brackets). Am I missing something here?

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  • $\begingroup$ "A magnetic field cannot be induced without a change in electric flux". Then how come a wire with steady current generates a magnetic field? Remember the displacement current term: $\nabla \times \mathbf{B} = \mu_0\left(\mathbf{J} + \epsilon_0\frac{\partial \mathbf{E}}{\partial t}\right)$ $\endgroup$ – Floris Aug 10 '17 at 14:39
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As the capacitor is being charged, the electric field between its plates is increasing with time. There is therefore a time varying electric flux aka a displacement current and, by Ampère's Law (which is, I believe, what you mean by "Maxwell's law of induction"), an MMF around the loop in your drawing.

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