Eight identical rectangular loops with their widths equaling twice their lengths

Question

Eight identical rectangular loops with their widths equaling twice their lengths are moving to the right in the vicinity of a region in which there is a uniform magnetic field coming out of the page. The rectangular loops are being pushed to the right at various constant speeds, as indicated on the diagram. The loops have various portions (25%, 50%, 75%, or 100%) within the field, as shown. Rank the magnitude of the rate of change of the magnetic flux through each loop at the instant shown from greatest to least. If several loops have equivalent values, please list them in alphabetical order.

Explanation / Answer

For A :

V = speed = 0.02 m/s

L = a

rate of change in magnetic flux = B L V = (0.02)aB

For B :

rate of change = 0       Since the area inside the magnetic field is not changing and is constant

For C :

V = speed = 0.04 m/s

L = a

rate of change in magnetic flux = B L V = (0.04)aB

For D :

rate of change in magnetic flux = 0      since the area inside the magnetic field is constant

For E :

rate of change in magnetic flux = 0      since the area inside the magnetic field is constant

For F :

V = speed = 0.02 m/s

L = 2a

rate of change in magnetic flux = B L V = (0.04)aB

For G :

V = speed = 0.06 m/s

L = a

rate of change in magnetic flux = B L V = (0.06)aB

For H :

rate of change in magnetic flux = 0      since the area inside the magnetic field is constant

G > F = C > A > B = D = E = H

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