Question

An electric generator contains a coil of 140 turns of wire, each forming a rectangular loop 71.2 cm by 22.6 cm. The coil is placed entirely in a uniform magnetic field with magnitude B = 4.32 T and initially perpendicular to the coil's plane. What is in volts the maximum value of the emf produced when the loop is spun at 1120 rev/min about an axis perpendicular to the magnetic field?

Answer 1

11405Volt

Step-by-step explanation:

To solve this problem it is necessary to use the concept related to induced voltage or electromotive force measured in volts. Through this force it is possible to maintain a potential difference between two points in an open circuit or to produce an electric current in a closed circuit.

The equation that allows the calculation of this voltage is given by,

`\epsilon = BAN \omega`

Where

B = Magnetic field

A= Area

N = Number of loops

`\omega`= Angular velocity

Our values previously given are:

`N = 140`

`A = 71.2*10^(-2)m*22.6*10^(-2)m=0.1609m^2`

`B = 4.32 T`

`\omega = 1120 rev / min`

We need convert the angular velocity to international system, then

`\omega = 1120 rev/min`

`\omega = 1120rev/min*(2\pi)/(1rev)*(1min)/(60sec)`

`\omega = 117.2rad/s`

Applying the equation for emf, we replace the values and we will obtain the value.

`\epsilon = BAN \omega`

`\epsilon = (4.32)(0.1609)(140)*117.2`

`\epsilon = 11405Volt`