Question 2.33: A lightning rod is a device that provides an attractive path...
A lightning rod is a device that provides an attractive path through a wire for lightning to discharge so that a building is hopefully protected. In order to attract the lightning to the rod, the path must originally have a low resistance. However, after the lightning stroke starts to discharge through this rod, the resistance should suddenly increase in order to protect the rod so it can survive to another day. Discuss how this could be done with inexpensive parts.
The lightning stroke will discharge through the shortest path between the two metal conductors as shown in (a). This discharge will act like a variable length conductor and will create a local magnetic field between the two metal conductors as depicted in (b). The direction of the resulting force (I dl x B from (2.145)) will cause this arc to move to the right where the path length becomes longer.
dF _{\text {magnetic }}= dQ ( \textbf v \times \textbf B )=\rho_{ v }( \textbf v \times \textbf B ) d v = \textbf J \times \textbf B ( ds )( dl )= \textbf I \textbf d \textbf I \times \textbf B (2.145)
Since the path length increases with motion of the arc to the right, the resistance will also increase. This device is called a lightning arrestor. The mechanism described here is also used in a device called a rail gun that may have applications of spewing forth “plasma bullets.” Movie aficionados should also recognize the Jacob’s ladders that appear in the laboratory of the old Dr. Frankenstein movies.