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Unit EEEN10028 Electromagnetic Fields
Lecturer Professor Anthony Peyton
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A d.p Stick contains two sma sphencal electrodes of radius, a separated by a distance of b meters. The stick ,s ubmerged .n water of conductivity a S/m, such that the electrodes can be assumed to be positioned almos vertically. A positive current of +1 Amps is injected into the upper electrode at (0, b/2) and an equal and opposite current -1 Amps flows out of the lower electrode at (0,-b/2). The layout is shown in the following diagram. Note the origin of the coordinate system is the mid-point between the two electrodes.
Insulating supports -*
Lower electrode
Water, a
Initlally the electrodes are deeply submerged so that c can be conskfered Inflnlte
a. Use superposition to how that the current dens.ty at a posmon (0,y) on the y-axis, where % - a |y| is given by
b. Derive an expression for the resistance of the water between the two ................................................................................
c. What ,s the resistance of a device with 2 mm diameter electrodes separated
by 2 cm submerged in sea water of conductivity 5 S/m.
This part is optional, if the depth is now considered to be finite:
d. What is the resistance of the electrode pair if the depth c is 1.5 cm?
Answers: c. 30.2 Q, d. 31.2 Q
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