A circular metal ring, as shown on the diagram below, isconstructed so as to exp

Question

A circular metal ring, as shown on the diagram below, isconstructed so as to expand or contract freely. In a region with aconstant magnetic field Bo oriented perpendicularto it, the ring expands, with its radius growing with timeas r=ro(1+t2).As the ring expands and grows thinner, its resistance per unitlength changes accordingto R=Ro(1+t2).Find the current induced in the ring as a function of time. Tocheck your answer, suppose that Bo =3.00 mT, ro = 10.0 cm,Ro = 8.00 [ /(m)], =0.110 × 10-4s2,and = 0.585 ×10-2s2. What isthe value of the induced current at t = 74.5 s?(Note: Give the direction of the current where when viewed fromabove a positive current will move counterclockwise.)
http://nplq1.phyast.pitt.edu/res/fsu/capalibrary/65EMInductionFaradayLenz/Graphics/prob05.gif

http://nplq1.phyast.pitt.edu/res/fsu/capalibrary/65EMInductionFaradayLenz/Graphics/prob05.gif

Explanation / Answer

magnetic flux = B*r2 induced emf = -d/dt = -2Br*dr/dt induced current I = /(2rR) =-2Br*(dr/dt)/(2rR) = -B(dr/dt)/R = -B(r0*2t)/[R0(1 +t2)] plug all known values and get I = -1.84*10-9 A

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