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?

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Chapter1: Units, Trigonometry. And Vectors
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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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