A circular metal ring, as shown on the diagram below, is constructed so as to ex

Question

A circular metal ring, as shown on the diagram below, is constructed so as to expand or contract freely. In a region with a constant magnetic field Bo oriented perpendicular to it, the ring expands, with its radius growing with time as r=ro(1+at2). As the ring expands and grows thinner, its resistance per unit length changes according to R=Ro(1+ßt2). Find the current induced in the ring as a function of time. To check your answer, suppose that Bo = 6.70 mT, ro = 15.0 cm, Ro = 1.85 [ ?/(m)], a = 0.115 × 10-4 s-2, and ß = 0.495 × 10-2 s-2. What is the value of the induced current at t = 85.0 s? (Note: Give the direction of the current where when viewed from above a positive current will move counterclockwise.) I'm not sure of the steps required to solve this problem. The way the question is worded is confusing to me so I am having a hard time finding an equation to solve for the induced current.

Explanation / Answer

as the metal ring expands there is an increase in the magnetic flux through the ring and hence there is some induced current the emf induced due to the changing area is d(p[ro(1+at2)]2*B)/dt solve the induced current in the ring is emf induced /resistance we know the resistance

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