Question

A coil of area 0:2 m2and total resistance 100 is rotated at a rate of 60 rev/s. Its axis ofrotation is perpendicular to a 0:5 T magnetic eld. How many turns are in the coil if energyis delivered to it at a maximum rate of 1420 W?

Answer 1

To solve this exercise it is necessary to apply the concepts given in the Faraday expressions and the induced voltage.

By definition the emf is given under the equation

$\epsilon =NBA\omega$

$\omega =$Angular Velocity

N = Number of Loops

B = Magnetic Field

A = Cross-Sectional Area.

At the same time we know that the rate of energy delivered is defined as,

$P = \frac{\epsilon^2}{R}$

$\epsilon = \sqrt{PR}$

Re-arrange the firs equation to find the number of loops and replacing the definition previously found we have,

$N = \frac{\sqrt{PR}}{BA\omega}$

$N = \frac{\sqrt{1420*100}}{0.5*0.2*(60*2\pi)}$

$N = 10$

Therefore the number of turns in the coild if energy is delivered to it at a maximum rate of 1420W are 10 loops.