I\'m lost on parts c and d... A)Consider a circular current loop of radius 10.5

Question

I'm lost on parts c and d...

A)Consider a circular current loop of radius 10.5 cm with 200 total turns. Assume that the current through the coil is I. What is the magnitude of the magnetic field at the center of the coil?

Ans: Bcenter=.001197I

B) A time-varying current of the form I(t)=I0sin(2pift) is passed through the circular coil in part a) whereIo= 10 mA. Using your result from a), write down the expression for the time varying magnetic field B(t) at the center of the coil.

Ans: B center (t)=(1.197x10^-5)sin(2pi*ft)

C) A small 1.5 cm radius circular current loop is placed at the center of the large current loop from part a) (as shown in the photo) oriented so that the plane of the current loop is perpendicular to the magnetic field. Assume that the magnetic field from the large current loop is constant over the small loop. What is the magnetic flux through the small current loop (use your result from part b).

D) What is the total induced emf in the small current loop assuming that it has 2000 turns (use your result from part c))? The frequency of the time-varying current is f=1000 Hz.(Your answer should be in the form of a numerical value times a trigonometric function of 2*pi*ft)

Explanation / Answer

C) total magnatic field inside loop = area of loop*magnatic field = pi*0.015*0.015*(1.197x10^-5)sin(2pi*ft) = 8.46*10^-9*sin(2pi*ft)

Magnetic flux = area*total magnetic field = pi*0.015*0.015*8.46*10^-9*sin(2pi*ft) = 5.98*10^-12*sin(2pi*ft) Answer

D) total flux from small loop = N*flux_due_to_each _loop = 2000*5.98*10^-12*sin(2pi*ft) = 1.196*(10^-8)*sin(2pi*ft)

EMF induced = -d/dt = -d(1.196*(10^-8)*sin(2pi*ft))/dt = -1.196*(10^-8)*2pi*f*cos(2pi*ft) =

-1.196*(10^-8)*2*pi*1000*cos(2pi*ft) = -7.515*10^-5*cos(2*pi*f*t) Answer

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