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The previous two exercises involved currents that are produced in conductors as a result of Faraday's law and they are given the name "eddy currents." If they arise from a time varying induction, it is possible to obtain a differential equation describing their properties. Begin by combining (17-10) and (12-25), and then by applying (1-120) show that, for steady currents, the eddy currents satisfy the equation $\nabla^{2} \mathbf{J}_{f}=$ $\sigma \mu_{0}\left(\partial \mathbf{J}_{f} / \partial t\right)$.

    The previous two exercises involved currents that are produced in conductors as a result of Faraday's law and they are given the name "eddy currents." If they arise from a time varying induction, it is possible to obtain a differential equation describing their properties. Begin by combining (17-10) and (12-25), and then by applying (1-120) show that, for steady currents, the eddy currents satisfy the equation $\nabla^{2} \mathbf{J}_{f}=$ $\sigma \mu_{0}\left(\partial \mathbf{J}_{f} / \partial t\right)$.

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Electromagnetic Fields

Electromagnetic Fields

Roald K. Wangsness 1st Edition

Chapter 17, Problem 16

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Step 1

Step 1: Combine (17-10) and (12-25) (17-10) is Faraday's law in differential form: $\nabla \times \mathbf{E} = -\frac{\partial \mathbf{B}}{\partial t}$ (12-25) is Ohm's law in differential form: $\mathbf{E} = \frac{1}{\sigma} \mathbf{J}_{f}$ We can substitute Show more…

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