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

\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}

Electromagnetic Induction. Maxwells Equations