I have attempted this problem several times and cannot seem to get the correct a

Question

I have attempted this problem several times and cannot seem to get the correct answer, so here goes:

A circular loop of flexible iron wire has an initial circumference of 166 cm, but its circumference is decreasing at a constant rate of 13.0 cm/s due to a tangential pull on the wire. The loop is in a constant uniform magnetic field of magnitude 0.800 T, which is oriented perpendicular to the plane of the loop. Assume that you are facing the loop and that the magnetic field points into the loop.

Find the magnitude of the EMF induced in the loop after exactly time 6.00 s has passed since the circumference of the loop started to decrease.
Express your answer numerically in volts to three significant figures.

Explanation / Answer

Let   circumference of the loop   circular loop C   =   2r   r = C / 2 And   area of the loop A   = r2   =    C2 / 4 dA/dt    = ( 2C / 4 )   dC/dt Here initail circumference C =   1.66 m ,   at   6sec     circumference C '   =   C -    t ( dC /dt  )   =                                                   = 1.66   - ( 6 ) ( 0.13 m/s)      = 0.88 m dC /dt   = 0.13m /s dA/dt   =    ( 2C' / 4 )   dC/dt magnetic field   B =   0.8 T Induced   emf   = d / dt     =   d( BA) / dt    = B * dA /dt   =   ( 0.8 T) ( 2*0.88m / 4 )    ( 0.13m /s )   = 0.0145 V

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