Changing Magnetic field inducing an electric field

[Silversonic]

Homework Statement

There is an infinite cylindrical cavity of radius 5m with a uniform magnetic field along the axis with an amplitude varying at some instant, with dB/dt = 0.05Ts^-1. Apply the integral form of Faraday's law and sketch the electric field induced in the plane perpendicular to the axis as a function of the distance from the centre r and evaluate it at r = 2m and r = 10m.

Homework Equations

$\oint$ E.dl = - $d/dt$$\int$B.dS

The Attempt at a Solution

What I don't understand here is how I would sketch the electric field. I've worked out the Electric field in the theta-hat direction (that would be the only component of E.dl that isn't canceled out) to be -0.05Vm^-1 for r=2 and -0.0625 Vm^-1 for r = 10.

How can the electric field be in the theta-hat direction? That makes no sense to me, it suggests the field lines are loops around the cylindrical cavity, and thus have no source or sink, which is an impossibility. But then again, E.dl only works out to give |E|dl where |E| would be in the theta-hat direction.

Anyone understand...? I don't.

 

[Spinnor]

That's cool, yes? The divergence of the electric field occurs when we have charge around, if there is no charge around then if there is electric field around the lines must close on themselves, see,

http://www.asiaman.net/androo/academics/TAing/phys24/week2/