Consider the following experiment, in which two people run across a football fie

Question

Consider the following experiment, in which two people run across a football field carrying a

length of wire (poorly sketched in perspective, below). The wire forms part of a continuous

rectangular loop, one end of which is fixed in place. Excess wire is curled up at the fixed end

of the loop, and unravels as the runners move away, such that the loop forms a rectangle that

progressively gets longer in the direction in which the runners move so long as there is spare

wire available. The runners are a distance R apart. The total length of the wire in the loop

(including the spare wire) is L. The wire has a resistivity ?, and a diameter d. The runners

move at a velocity v. The vertical component of the earth

Explanation / Answer

a)

= B0 R v

resistance = r = L/a = L/( (d/2)2) = 4 L/( d2)

i = /r = B0 R v/(4 L/( d2)) = d2 B0 R v/(4 L)

b)

anticlockwise

c)
F = i R B = ( d2 B0 R v/(4 L)) R B0 = d2 B02 R2 v/(4 L)

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