The Washington monument is 555 ft. tall. A mad scientist places a wire from a po

Question

The Washington monument is 555 ft. tall. A mad scientist places a wire from a point on the ground (directly south of the monument) to the top of the monument, such that the wire makes an angle of 20 degree to the horizontal. Using trig, find the length of the wire in meters. The mad scientist now waits for a lightning strike. A typical strike is around 30 kA. Knowing that the Earth creates a magnetic field of 5 times 10^-5 T on the Earth's surface, find the force on the wire during a lightning strike due to this B field.

Explanation / Answer

part a:

sin(20)=height/length

==>length=height/sin(20)=555/sin(20)=1622.7 ft

hence length of the wire is 1622.7 ft=494.6 m

part b:

force on the wire=current*cross product of length vector and magnetic field vector)

length vector is directed along the directon of current

hence force=current*length*magnetic field*sin(20)

=30*1000*5*10^(-5)*494.6*sin(20)=253.74 N

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