Magnitude and Direction of a Magnetic Field at the Circumference of a Disk

[GermanMC]

Homework Statement

A very thin disk of non-conducting material initially holds a charge Q_O = +5 μC that decreases with time t as

Q(t) = Q_O e^-t/τ
where τ = 10 seconds.
If the disk has a radius of 0.10 m, what is the magnitude and direction of the magnetic field at the circumference of the disk as a function of time?

Homework Equations

Assume at any time t that the displacement vector D is uniform across the disk.
There is no free current.

∇$\bullet$E = (1/ε_O)ρ

∇×B = μ_OJ + μ_Oε_O (∂E/∂t)

The Attempt at a Solution

I tried to just work out the curl of B and I immediately ran into problems and it's not correlating to the problem.

 

[vela]

Show your work. Don't just describe what you did generally.