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A current l = 1.5 A is flowing through a...

A current l = 1.5 A is flowing through a long solenoid of diameter 3.2 cm, having 220 turns per cm. At its centre, a 130 turn closely packed coil of diameter 2.1 cm is placed such that the coil is coaxial with the long solenoid. The current in the solenoid is reduced to zero at a steady rate in 25 ms. What is the magnitude of emf induced in the coil while the current in the solenoid is changing?

Text Solution

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Initially magnetic flux passing through the coil (one turn),
`pi_(1)= barB . barA= BA cos0^(@)`
`= mu_(0)nl xx (pi d^(2))/(4)`
`= 4pi xx 10^(-7) xx 1.5 xx 22000 xx 3.464 xx 10^(-4)`
`1.44 xx 10^(-5) Wb`
Finally the flux becomes zero because the current reduces to zero. Thus, `e= (|Delta phi |)/( Delta t)= (1.44 xx 10^(-5))/(25 xx 10^(3))= 5.76 xx 10^(-4) V`
`"The total emf"= N xx e`
`= 130 xx 5.76 xx 10^(-4)= 75 mV`
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