# Can anyone draw the Field Lines of Faraday induced electric field

Tags:
1. Oct 29, 2014

### 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.

2. Oct 29, 2014

### Staff: Mentor

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
$E=-\nabla \phi-\partial A/\partial t = (y~df/dt, -x~df/dt,0)$

Last edited: Oct 29, 2014
3. Oct 29, 2014

### 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?

4. Oct 29, 2014

### Staff: Mentor

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.

5. Oct 29, 2014

### AbhiFromXtraZ

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

6. Oct 29, 2014

### 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.

7. Oct 30, 2014

### Staff: Mentor

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

8. Oct 30, 2014

### 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?