Emf / coil induction from a spark

[elegysix]

Homework Statement

suppose we have a coil sitting on a desk (with radius =1), and then a spark passes by the side of it, in such a way that the magnetic flux through the coil is maximized. The coil is attached to a full wave rectifier which is connected to a very large capacitor.

There is an initial potential difference of 1.94MV, which causes the air to break down and creates a 2m long spark.Find the average V and maximum V in the coil during dielectric breakdown

How much power can the coil produce from the spark?

Homework Equations

B(R,t)\approx\frac{\mu_{0}I(t)}{2\pi R} (in the region of the coil)

\Phi_{B}(t)=\oint B(R,t) \bullet ds

V(t)=N\frac{d\Phi_{B}(t)}{dt}

The Attempt at a Solution

I know that the V in the coil depends on \frac{d\Phi_{B}}{dt}
and B depends on the current, but since this is a spark, I don't know how to say what the current is...

I think \frac{d\Phi_{B}}{dt} will be very large since the time is almost instantaneous, but I have no idea how to handle a spark as a current.

This is not for class, but just to satisfy my curiosity

any help would be greatly appreciated!

thanks!

 

[Delphi51]

I don't think there is enough information to calculate the answer.
Possibly the initial current could be calculated by looking up some characteristics of air but you need information about how it varies over time in order to complete the calculation. That depends very much on the source of the initial voltage causing the spark. Is it a constant V from a battery? Or something varying with time? If varying, how does it vary with time? You can't find the derivative with respect to time unless you have the function of time to work with.

There is also the matter of the size of the spark. That will affect the distance of the current from the coil and the strength of the magnetic field inside the coil.

 

[elegysix]

suppose the spark occurs between two needle points, separated by 10 cm. The coil near it is 10 mm in diameter, with 10 turns. The voltage across the points builds very slowly until a spark occurs.

I have no idea the voltage between points after the discharge, is there a way to work around that?

 

[I like Serena]

Hmm, I believe the orientation of the magnetic field will be off.
This means no (significant) current is induced in the coil.
And after tweaking the orientation of the coil to pick up some magnetic field changes, I'm afraid the problem offers too little information to calculate V.

 

[elegysix]

what more would you need to know?