Brief question about induced electric fields

[bayners123]

Homework Statement

We have a solenoid with current I and n turns per unit length and (neglecting hysteresis) a ferromagnetic core. Find B and H.
Show that when I is varied an electric field is induced and draw it on a diagram.

Homework Equations

$$\nabla \times E = - \frac{\partial \bar{B}}{\partial{t}}$$

The Attempt at a Solution

Finding B and H is fine: they come to $$\bar{B} = \mu_r \mu_0 n I \hat{\underline{z}}$$
so $$\frac{\partial \bar{B}}{\partial t} = \mu_r \mu_0 n \frac{\partial I}{\partial t} \hat{\underline{z}}$$.
This implies that when I changes positively an electric field is induced such that the curl of it is in the opposite direction to H.

What I wanted to ask was does this mean that you get an electric field inside the solenoid that sort of goes around in a circle but in the opposite direction to I? I couldn't find it on the internet anywhere so I thought I'd ask to be sure. I've done a (rubbish) diagram of what I mean at http://users.ox.ac.uk/~quee2327/photo.JPG . The magnetic field is meant to be coming out of the page.

 

[Quinzio]

This implies that when I changes positively an electric field is induced such that the curl of it is in the opposite direction to H. What I wanted to ask was does this mean that you get an electric field inside the solenoid that sort of goes around in a circle but in the opposite direction to I?

Yes, it does.

 

[bayners123]

Great, thanks! I just wasn't sure of my maths.