Patients undergoing electrosurgery sometimes suffer bums around the perimeter of

Question

Patients undergoing electrosurgery sometimes suffer bums around the perimeter of the electrode. Wiley and Webster (1982) analyzed the potential produced by a circular disk electrode of radius a and potential v_0 in contact with a medium of conductivity sigma. They found that the normal component of current density at the surface of the electrode is given by Calculate the total current I coming out of the electrode. Determine the resistance of the electrode. Plot j_n vs. r. Use the plot to explain why the patients suffer burns near the edge of the electrode.

Explanation / Answer

A)

The total current is equal to the current desity multiplied by the Area of the disk. So:

A=Pi(a)^2

I=2(sigma)(Vo)(a^2) / (a^2-r^2)^(1/2)

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2) Using Ohm's law: R=V/I we get:

R= (Vo)/(2(sigma)(Vo)(a^2)/(a^2-r^2)^(1/2))

R=(a^2-r^2)^(1/2) / 2(sigma)(a^2)

3)

It is a sort of parabola that opens up. It starts at r=0, J=(2sigmaVo)/Pi and as R increases, Jn increases even more. When R=a the value of Jn is infinite (When it is close to a, the value of the Electric current density is very high!)

Here is the graph:

http://fooplot.com/plot/shke1njooz

a=1

and (2sigmaVo)/pi is also = 1

(This does not affect the behaviour of the graph)

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