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A horizontal circular wire loop of radius 0.5 m lies in a plane perpendicular to a uniform magnetic field that is pointing down from above into the plane of the loop, and has a constant magnitude of 0.45 T. If in 0.14 s the wire is reshaped from a circle into a square, but remains in the same plane, what is the magnitude of the average induced
emf in the wire during this time? (Hint: what remains constant during the change is the total length of the wire that formed the initial loop.] Answer in units of V.

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Answer:

Explanation:

Area of circle = 3.14 x0 .5 x0 .5 = 0.785 m² .

Length of side of square  formed = 2 x 3.14 x .5 /4 = 0.785 m

Area of square = .785 x .785

So there will be decrease in area on circle becoming square.

Change in area = .785 - .785² = .168775 m²

change in flux = .168775 x .45 = .076 web

emf induced =  -dΦ/dt = .076/ 0.14 = 0.54 V.

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