Refer to diagram 3. A closed circular loop (N = 555 turns, radius r= 5.54 cm, resistance R = 6.32 2) sits in a magnetic field B pointing perpendicular to the plane of the loop and into the page. The magnitude of the magnetic field changes with time according to: 3 = 3.75t2 + 5.44t + 97.9, where B is in T and t is in seconds. After 0.578 seconds, find I, the current induced in the loop, in A. Give the answer as positive if the current runs clockwise in the loop, and negative if the current runs counter-clockwise.
Refer to diagram 3. A closed circular loop (N = 555 turns, radius r= 5.54 cm, resistance R = 6.32 2) sits in a magnetic field B pointing perpendicular to the plane of the loop and into the page. The magnitude of the magnetic field changes with time according to: 3 = 3.75t2 + 5.44t + 97.9, where B is in T and t is in seconds. After 0.578 seconds, find I, the current induced in the loop, in A. Give the answer as positive if the current runs clockwise in the loop, and negative if the current runs counter-clockwise.
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From figure we can see the magnetic field is directed downward and from the given equation for magnetic field we can see it is increasing with time. Therefore magnetic flux passes through the loop also increases with time. Therefore the direction of induced current will be in such a way so that magnetic field due to this current must be opposite to the direction of applied magnetic field, and this is possible only if direction of induced current counter-clockwise.
Therefore induced current is directed in counter-clockwise direction.
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