A square with sides of length 137 meters is placed in the x-y plane in a magneti

Question

A square with sides of length 137 meters is placed in the x-y plane in a magnetic field directed in the +z direction It is wound once and its resistance is4 Ohms. The initial magnetic field is 1.8 Tesla. The magnetic field is then changed in 2 sand the average induced current is 8 amps running clockwise. First, find the final magnetic field to needed to induce this average current. Then, the magnetic field (still in the +z direction) is held constant at the value of the final magnetic field that was just found. Then, the wire is reshaped into a circle that is wound once in a time of 5 seconds. If the resistance does not change, what is the average induced current, in amps, when the wire changes shape? If it's clockwise include a negative sign.

Explanation / Answer

magnetic flux = N*B*A1 = N*B*l^2

induced emf = rate of change in flux

e = (d/dt)*N*B*A = N*A*(dB/dt)

current i = e/R

dB = B2 - B1

dt = 2 s

8 = (1*1.37^2*(B2-1.8)/2)/4

B2 = 36 T <<<<<_________________ANSWER

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now area is changed

A2 = pi*r^2

length of the square = lenght of the circle

4*l = 2*pi*r

r = 2l/pi

r = (2*1.37)/pi

r = 0.873 m

emf = N*B2*(dA/dt)

e = N*B2*(pi*r^2 - l^2)/dt

e = 1*36*(pi*0.87^2-1.37^2)/5 = 3.61 V

current i = e/R = 3.61/4 = -0.9 A <<<----------answer

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