6. A loop of a wire has the shape shown in the drawing. The top part of the wire

Question

6. A loop of a wire has the shape shown in the drawing. The top part of the wire is bent into a semicircle of radius r 0.16 m. The normal to the plane of the loop is parallel to a constant magnetic field of magnitude 0.60 T. What is the magnitude of the change in the magnetic flux that passes through the loop when, starting with the position shown in the drawing, the semicircle is rotated through quarter of a revolution? Wb (into paper) 7. A circular coil of radius 4.00 cm contains 110 loops and its plane is positioned perpendicular to a uniform 0.42-T magnetic field, as shown. It is quickly and uniformly pulled from the field to a region where the B-field drops abruptly to zero. It takes 0.10 s for the whole coil to reach the field-free region. How much power is dissipated in the coil if its resistance is 110 ?

Explanation / Answer

area of semicircle pi*r^2/2

flux = B*A*costheta

loop is rotated from theta1 = 0   to   theta2 = 90

change in flux = BA*costheta1 - B*A*costheta2

change in flux = 0.6*pi*0.16^2/2*cos0 - 0 = 0.024 Wb

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7)

flux through the loop = N*B*A

induced emf = rate of change in flux

e = N*B*A/t

N = number of turns

B = magnetic field

A = pi*r^2

r = radius of loop

e = 110*0.42*pi*0.04^2/0.1

e = 2.32 v

power dissipated P = e^2/R

P = 2.32^2/110

P = 0.0489 W

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