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## Homework Statement

Figure 26-30 shows a swimmer at distance D=35m from a lightning strike to the water, with current I=78kA. The water has resistivity 30 Ohm*m, the width of the swimmer along a radial line from the strike is 0.7m, and his resistance across that width is 4 kOhm. Assume that the current spreads through the water over a hemisphere centered on the strike point. What is the current through the swimmer?

## Homework Equations

V = IR

R = pL/A

Surface area of a hemisphere = 2*pi*r^2

## The Attempt at a Solution

Assume the swimmer has a body surface area of 'A' underwater.

Then the resistance of a hypothetical 'wire' of seawater with cross-sectional area A will be p*L/A = 30*35/A

The current through this 'wire' will be the current of the lightning strike multiplied by the fraction of the surface area of the hemisphere occupied by the swimmer: Iwire = Istrike*(A/(2*pi*L^2)) = (78,000*A)/(2*pi*35^2)

The voltage applied to the swimmer is V = IR = (78,000*A*30*35)/(2*pi*35^2*A). The area of the swimmer cancels out and V is approximately 10,640 volts.

Then the current through the swimmer is I = V/R = 10,640/4000 = 2.66 A.

Did I make a mistake by not using the radial width of the swimmer? Also, my solution implies that the current through a swimmer is proportional to 1/R, where R is the distance between the swimmer and the lightning strike. Is that the right end behavior?

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