I\'m not entirely certain how to begin and work thisproblem. In a circular loop

Question

I'm not entirely certain how to begin and work thisproblem. In a circular loop in the plane of the paper lies in a 1.0 Tmagnetic field pointing into the paper. If the loop's diameterchanges from 20 cm to 6 cm in 0.5 seconds, (a) what is thedirection of the induced current, (b) what is the magnitude of theaverage induced EMF, and (c) if the coil resistance is 10,what is the average induced current? Please help!! I'm not entirely certain how to begin and work thisproblem. In a circular loop in the plane of the paper lies in a 1.0 Tmagnetic field pointing into the paper. If the loop's diameterchanges from 20 cm to 6 cm in 0.5 seconds, (a) what is thedirection of the induced current, (b) what is the magnitude of theaverage induced EMF, and (c) if the coil resistance is 10,what is the average induced current? Please help!!

Explanation / Answer

The circular loop lies in the plane of the paper with amagnetic field B = 1.0 T pointing into the paper The loop's diameter changes from 20 cm to 6 cm in 0.5seconds (a)According to Ampere's right hand thumb rule,if the thumb ofthe right hand points in the direction of the current flow,then thecurling of fingers indicates the direction of the magneticfield. Here,the magnetic field points into the paper,therefore,theinduced current in the circular loop flows in the leftdirection. (b)The magnitude of the average induced EMF is E = B * l * v ---------------(1) Here,l = 2r,where r = (20 - 6) cm = 14 cm = 14 *10-2 m and v = r * w,where w = (2/T),where T = 0.5s Susbtituting the above values in equation (1),we get E = B * 2r * r * w or E = 2 * B * r2 * w or E = 2 * 3.14 * 1.0 * (14 * 10-2)2 *(2 * 3.14/0.5) or E = 1.5 V (c)The average induced current in the coil is I = (E/R) Here,R = 10 or I = (1.5/10) = 0.15 A

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