Where do Faraday induced electric field lines curl when magnetic field turns off

[AbhiFromXtraZ]

Suppose there is an uniform magnetic field along z-direction. Now someone turns off the field. Then there will be an induced electric field.
Can anybody draw this induced electric field lines?
I know the electric field will curl around. But where will be the centre of that curl.
Do the electric field lines curl around the individual magnetic field lines or anything elese.
If I consider a loop of wire then I can easily answer using Flux Rule or Lenz's law.
But I want the field lines without considering any loop.
Thanks.

 

[Dale]

For a scalar potential $\phi=0$ and a vector potential $A=(-y~f(t),x~f(t),0)$ we have:
$B=\nabla \times A = (0,0,2f)$
and
$E=-\nabla \phi-\partial A/\partial t = (y~df/dt, -x~df/dt,0)$

 

[AbhiFromXtraZ]

Can you show me the picture of the electric field lines if the magnetic field was constant and along z-direction and suddenly turned off?

 

[Dale]

You can get the picture from the equations I posted. Use a graphing software or even do it by hand. It should only take a couple of minutes.

 

[AbhiFromXtraZ]

ok...I have to figure it out...Thanks !

 

[willem2]

This problem doesn't have an answer. An electric field:

$$E_x = (y-y_0) \frac {dB_z}{dt}$$
$$E_y = -(x-x_0) \frac {dB_z}{dt}$$
$$E_z = 0$$

will work for every x0 and y0, and this can produce any magnitude and any direction (in the xy plane) for E.

 

[Dale]

Yes. I chose $\phi=0$ for convenience, but any $\phi$ would also be a solution.

 

[AbhiFromXtraZ]

willem2, I think you are missing appropriate boundary conditions. Am I right? Well, if the magnetic field was generated from a long solenoid of radius 'r' , then would the electric field curl around the axis of the solenoid?