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

AI Thread Summary
The discussion focuses on calculating the average induced voltage in a rotating wire within a magnetic field. The parameters include a wire with 20 turns, an area of 400 cm², a magnetic field strength of 0.3 T, and a rotation speed of 10 rotations per second. The user applies Faraday's Law and calculates the magnetic flux and induced voltage, arriving at an answer of 9.6 V. However, there is a suggestion that the rotational speed was not adequately considered in the calculations. The discussion highlights the need to incorporate the angular velocity in the formula for accurate results.
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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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you did not include the rotational speed

E=d/dt(NBAcostωt)

remember θ=ωt
 

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