e coil at a time of t= 1.1 s at distance r= 0.22 m from the center of the solenoid if there are, n=119 turns/m?

Physics for Scientists and Engineers, Technology Update (No access codes included)
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Author:Raymond A. Serway, John W. Jewett
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Chapter31: Faraday’s Law
Section: Chapter Questions
Problem 31.54AP: A circular loop of wire of resistance R = 0.500 and radius r = 8.00 cm is in a uniform magnetic...
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The current I through a long solenoid with n turns per meter and radius 0.30m is changing with time as given by I=sin(120t). The magnetic field inside a solenoid is given by B=nμ0I where μ0 is the free space permeability μ0=1.26·10−6 H/m. 

What is the magnetic flux through a single coil at a time of t= 1.1 s at distance r= 0.22 m from the center of the solenoid if there are, n=119 turns/m?

a) Start by determining the flux through a gaussian loop of radius r=0.22 m centered in the middle of the solenoid. 

b) Next determine the rate of change of the magnetic flux with time

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