- #1

- 14

- 0

## Homework Statement

From an original surface current ##\vec{K}=K\hat{\phi}## on a finite solenoid, I got ##\vec{B}=\mu_{0}Kf(z)\hat{k}##, for ##r<R##. Assuming that ##\vec{K}## now slowly oscillates in time such as: ##\vec{K(t)}=K_{0}\cos\left(\omega t\right)\hat{\phi}##, so that I still can use the original expression for ##\vec{B}##, how can I find ##\vec{E}##?

## Homework Equations

Maxwell's Equations

## The Attempt at a Solution

Since ##\vec{B}=B_{k}(z)\hat{k}##, then: ##\nabla\times\vec{B}=0##, thus ##\frac {\partial{\vec E}} {\partial t}=\frac{-\vec{J}}{\epsilon_{0}}##.

Also, ##\nabla\times\vec{E}=\mu_{0}K_{0}f(z)\omega \sin\left(\omega t\right)\hat{k}##

How can I find the x and y components of ##\vec{E}##?