Electromotive Force in Spiral
المؤلف:
Sidney B. Cahn Boris E. Nadgorny
المصدر:
A GUIDE TO PHYSICS PROBLEMS
الجزء والصفحة:
part 1 , p 60
9-8-2016
1975
Electromotive Force in Spiral
A flat metal spiral (with a constant distance h between coils) and a total number of coils N is placed in a uniform magnetic field B = B0 cos ωt perpendicular to the plane of the spiral (see Figure 1.1). Evaluate the total electromotive force induced in the spiral (between points A and C). Assume N >> 1.
Figure 1.1
SOLUTION
The electromotive force εe is given by
(1)
where Φ is the magnetic flux, and we used r(φ) = hφ/2π. As another solution, in the approximation of a large number of coils, we can consider the nth coil to be a circle of radius rn = nh. Then,
where Sn = πr2n = πh2n2 is the area of the nth coil. So we find for the electromotive force between the ends of a single coil
(2)
Summing up over all the coils from (2), we obtain the total electromotive force (1)
(3)
where we have used the approximation
for N >> 1.
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