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Two concentric and coplanar circular coils have
radii a and b (>> a) as shown in figure. Resistance
of the inner coil is R. Current in the outer coil is
increased from 0 to i, then find the total charge

circulating the inner coil.

sir, please explain how u calculated flux

Asked by jaychandran1967 29th September 2018, 7:10 PM
Answered by Expert
Answer:
induced emf e in the coil is given by,  e = -(dφ/dt) , where φ is flux of magnetic field.
 
induced current i = e/R = begin mathsize 12px style equals space minus space 1 over R fraction numerator d phi over denominator d t end fraction end style, where R  is resistance of coil
charge circulating in th coil  Q = | i×dt | = dφ/R = (1/R) d( B×A)  .................(1)
where B is flux density of magnetic field, A is area of coil.
 
magnetic field flux density B inside the coil of radius a is given by, B begin mathsize 12px style equals space fraction numerator mu subscript 0 space cross times space i over denominator 2 a end fraction end style
In eqn.(1), Area A is constant and by substituting for B, we get    begin mathsize 12px style Q space equals space open parentheses A over R close parentheses fraction numerator mu subscript 0 over denominator 2 a end fraction d i end style............................(2)
in Eqn.(2), di is change in current 0 to i, hence we can write di = i to get charge Q
 
Hence begin mathsize 12px style Q space equals space open parentheses A over R close parentheses fraction numerator mu subscript 0 over denominator 2 a end fraction cross times i end style
Answered by Expert 4th October 2018, 2:04 AM
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