In an oceanographic experiment two long, coaxial electrodes are inserted into se

Question

In an oceanographic experiment two long, coaxial electrodes are inserted into sea water and the resistance between them is measured. If the inner cylinder has diameter a and the outer cylinder has diameter 3a, the resistance can be expressed as R=fp/r where L = length of the cylinders and r =r esistivty of sea water.What is the value of the numerical factor f? Derive the formula for the resistance between two coaxial cables in general and for the oceanographic experiment. The outer diameter is a and the inner diameter is b. HINT: You must use some of Maxwell's equations and integrate.

Explanation / Answer

The resistance can be expressed as R = fL/r ........ (1) from the equation 1 the derived formula for f is f = Rr/L   ...........   (2) here Resistance R can be R = L/A plug the value of R in equation 2 hence f = r /A ........ (3) A is the difference in area of the cylinders = (3a/2)2-(a/2)2                                                                     = 2a2 now the equaiton 3 can be written as f = r/2a2   ...........     (4) here is resistivity of electrodes (which are used ) r is the resistivity of sea water a is diameter plug all the parameters in equation 4 to get factor f . The resistance can be expressed as R = fL/r ........ (1) from the equation 1 the derived formula for f is f = Rr/L   ...........   (2) here Resistance R can be R = L/A plug the value of R in equation 2 hence f = r /A ........ (3) A is the difference in area of the cylinders = (3a/2)2-(a/2)2                                                                     = 2a2 now the equaiton 3 can be written as f = r/2a2   ...........     (4) here is resistivity of electrodes (which are used ) r is the resistivity of sea water a is diameter plug all the parameters in equation 4 to get factor f .                                                                     = 2a2 now the equaiton 3 can be written as f = r/2a2   ...........     (4) here is resistivity of electrodes (which are used ) r is the resistivity of sea water a is diameter plug all the parameters in equation 4 to get factor f .

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