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
[tex]\epsilon = NBA\omega[/tex]
Where
N = Number of loops
B = Magnetic Field
A = Cross-sectional Area
[tex]\omega =[/tex] Angular velocity
Re-arrange to find N,
[tex]N = \frac{\epsilon}{BA\omega}[/tex]
In parallel, we can also consider the rate of energy change expressed in terms of the induced voltage, that is,
[tex]P = \frac{\epsilon^2}{R}[/tex]
Where
R = Resistance
The previous equation can be expressed as
[tex]\epsilon=\sqrt{PR}[/tex]
Equating the two expression we have
[tex]N = \frac{\sqrt{PR}}{BA\omega}[/tex]
Replacing with our values we have that
[tex]N = \frac{\sqrt{(1420)(100)}}{(0.5)(0.2)(60*2\pi)}[/tex]
[tex]N=9.9957 \approx 10[/tex]
Therefore the number of turns are 10.
