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

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Physics

9. A cow is standing in a flat field, with its front legs at thedistance L from a lone tree. The cow is facing the tree, and theseparation between its front and hind legs is D. It is gentlyraining and the ground is damp, with resistivity ρ. A lightningstrikes the tree, for an instant providing a constant current Iinto the ground. The rest of the problem is concerned with whathappens to the cow. (No animals were harmed in the creation of thisproblem, although unfortunately the situation described here issomewhat realistic.)

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

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

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

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