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Electromagnetic Induction. Maxwells Equations

Problem 3.308

In a long straight solenoid with cross-sectional radius \(a\) and number of turns per unit length \(n\) a current varies with a constant velocity \(\dot{I}\) A/s. Find the magnitude of the eddy current field strength as a function of the distance \(r\) from the solenoid axis. Draw the approximate plot of this function.

Reveal Answer
E={1/2μ0nI˙r for r<a1/2μ0nI˙a2/r for r>aE=\left\{\begin{array}{ll} 1 / 2 \mu_{0} n \dot{I} r & \text { for } r<a \\ 1 / 2 \mu_{0} n \dot{I} a^{2} / r & \text { for } r>a \end{array}\right.
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