Acoil of area 0.2 m2 and total resistance 100 ω is rotated at a rate of 60 rev/s. its axis of rotation is perpendicular to a 0.5 t magnetic field. how many turns are in the coil if energy is delivered to it at a maximum rate of 1420 w?

The concept necessary to solve this problem is the mathematical definition of the electromotive force or induced voltage. Theoretically the electromotive force is the electrical action produced by a non-electrical source. Mathematically it can be expressed as

Where

N = Number of loops

B = Magnetic Field

A = Cross-sectional Area

Angular velocity

Re-arrange to find N,

In parallel, we can also consider the rate of energy change expressed in terms of the induced voltage, that is,

Where

R = Resistance

The previous equation can be expressed as

Equating the two expression we have

Replacing with our values we have that

Therefore the number of turns are 10.

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