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Electromagnetic Induction. Maxwells Equations

Problem 3.351

A long straight solenoid has \(n\) turns per unit length. An alternating current \(I=I_{m} \sin \omega t\) flows through it. Find the displacement current density as a function of the distance \(r\) from the solenoid axis. The cross-sectional radius of the solenoid equals \(R\).

Reveal Answer
 3.351. jd={1/2B¨r for r<R,1/2B¨R2/r for r>R. Here B¨=μ0nImω2sin⁡ωt\begin{aligned} &\text { 3.351. } j_{d}=\left\{\begin{array}{l} 1 /{ }_{2} \ddot{B} r \quad \text { for } r<R, \\ 1 /{ }_{2} \ddot{B} R^{2} / r \text { for } r>R . \end{array}\right.\\ &\text { Here } \ddot{B}=\mu_{0} n I_{m} \omega^{2} \sin \omega t \end{aligned}
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