A coil of wire (61.163 cm^2 area) can generate a voltage difference when rotated in a magnetic field. If a 904 turn coil is rotated at 65 Hz in a B field of 0.001 T, what is the voltage created ?

Respuesta :

Answer:

[tex]EMF_{max} = 2.26 Volts[/tex]

Explanation:

As we know that the rotating coil will have change in the angle with time at all instant of time

so at any general instant of time we can say

[tex]\phi = NBA cos\omega t[/tex]

now we have

[tex]EMF = \frac{d\phi}{dt}[/tex]

so we have

[tex]EMF = NBA\omega sin\omega t[/tex]

so we have maximum induced EMF in the coil is given as

[tex]EMF_{max} = NBA\omega[/tex]

[tex]EMF_{max} = (2\pi f)NBA[/tex]

N = 904 turns

B = 0.001 T

[tex]A = 61.163 cm^2 = 61.163 \times 10^{-4} m^2[/tex]

f = 65 Hz

now we have

[tex]EMF_{max} = (904)(0.001)(61.163 \times 10^{-4})(2\pi\times 65)[/tex]

[tex]EMF_{max} = 2.26 Volts[/tex]