# Separating the convective and the inductive electric field

My question is basically this, if I am only able to measure the total electric field and the magnetic field at a few discrete points in space and time, is it possible to separate the convective and the inductive electric field?

Here is the background. Consider the geomagnetosphere. There is a background geomagnetic field. There is a convective background electric field. Now picture a bunch of charged particles in addition with various energies and velocities so they are guided by the fields and in return modify the fields and so on. There are also other oscillations in both fields introduced from outside. So now we have an induced electric field. I then throw a satellite in there which reports the total magnetic field vector and the total electric field vector but these are only discrete values in space and in time and I have a very small sample of the entire magnetosphere.

Is this even theoretically possible? It seems like at least some theoretical work must have been done on this. If someone can nudge me in the right direction or point to some references, it will be a great help.

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Is the induced electric field generated by periodically changing magnetic field ? Is the induced electric field itself constant or not ? – Rijul Gupta Jan 13 '14 at 8:17
@rijulgupta No to both questions. In fact, you can think of the oscillations of both fields as random and the range of the frequencies and amplitudes varies widely. The spectrum is definitely continuous. – Fixed Point Jan 13 '14 at 9:15
Isn't it possible that you measure the constant magnetic and/or electric field at various points before the particles are released ? – Rijul Gupta Jan 13 '14 at 9:19
@rijulgupta Sorry, the above description is something like "imagine the background fields....and then particles enter the picture...etc". The particles are always there and we have no control over them. We don't literally release the particles. So nope, we can't measure the fields without the particles being present. – Fixed Point Jan 13 '14 at 9:55

Yes !! I have found a solution which makes it theoretically possible and should work out practically just as well.

● You say you can measure the net electric and magnetic field at a particular point lets call them $E$ and $B$.
● Now since the charged particles are moving haphazardly they will produce both time varying electric and magnetic field lets call them $E'$ and $B'$.
● There also exist constant electric and magnetic field lets say $E_0$ and $B_0$ so the equations must be:

$E = E_0 + E'$
$B = B_0 + B'$

For an area in which these fields are measured.
$\Phi_B = \Phi_{B_0} \Phi_{B'}$

Since the constant magnetic field does not change, its flux does not change as well.
$\Delta \Phi_B = \Delta \Phi_{B'}$
.
taking change in magnetic field in small time and dividing it by change in time, we get :
$\frac{d\Phi_B}{dt} = \frac{d\Phi_{B'}}{dt} = E'$
Since induced magnetic and electric fields are interelated by time differential of their corresponding flux.

Similarly, you can also have,
$\frac{d\Phi_E}{dt} = \frac{d\Phi_{E'}}{dt} = B'$

Using above equations you can first find the induced electric and magnetic fields and then subtract then from net fields to get constant non-induced fields.

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Wow, looks promising. This should work. Thanks for the help. – Fixed Point Jan 18 '14 at 1:02