9. A cow is standing in a flat field, with its front legs at the distance...

9. A cow is standing in a flat field, with its front legs at the distance L from a lone tree. The cow is facing the tree, and the separation between its front and hind legs is D. It is gently raining and the ground is damp, with resistivity ρ. A lightning strikes the tree, for an instant providing a constant current I into the ground. The rest of the problem is concerned with what happens to the cow. (No animals were harmed in the creation of this problem, although unfortunately the situation described here is somewhat realistic.)

(a) Assuming that the current spreads from the base of the tree into the ground (which we will treat as homogeneous) in all three dimensions, calculate the current density at the distance r from the base of the tree.1

(b) What is the voltage between the cow’s front and hind legs?

(c) The cow can sustain a maximal voltage of Vmax between the front and hind legs. What is the minimal distance Lmin that the cow needs to stand from the tree to survive the lightning strike?

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Expert Solution

genius_generous answered 8 months ago

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