E=d/dt(NBAcostθ) Magnetic Field Induced by Rotating Wire in Uniform Field

In summary, the average magnetic field induced in a 20 turn wire rotating at a speed of 10 rotations/second, with a surface area of 400cm^2 and a uniform magnetic field of 0.3T, can be calculated using Faraday's Law by finding the change in magnetic flux over time. The answer is 9.6 Volts. However, there may be an error in the calculation if the rotational speed was not included.
  • #1
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Homework Statement



A 20 turn wire that has a surface of 400cm^2 is rotating around an axe and is at a right angle to a uniform magnetic field of 0.3T. Find the average magnetic field induced if the speed of the rotation is 10 rotations/second.


Homework Equations



Faraday's Law


The Attempt at a Solution



A = 400cm^2 = 0.04m^2
N = 20
B = 0.3T
f = 10Hz



V =(Nxdelta phi)/delta t
B = phi/A
phi = BA = 0.3x0.04 = 0.012wb
V= (20x0.012)/0.1 = 2.4 Volts


Answer = 9.6 V

Can anyone point out where my error is? If there isn't any its possible the answer is wrong.
 
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  • #2
you did not include the rotational speed

E=d/dt(NBAcostωt)

remember θ=ωt
 

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Electromagnetism is a branch of physics that deals with the study of the relationship between electricity and magnetism. It is based on the concept that electric currents create magnetic fields and vice versa.

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