Through a long solenoid of diameter `4.1` cm, having 100 turns per cm, a current I = 1A is flowing. At its centre, a 60 turns closely packed coil of d
Through a long solenoid of diameter `4.1` cm, having 100 turns per cm, a current I = 1A is flowing. At its centre, a 60 turns closely packed coil of diameter `3.1` cm si 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 10 ms. What is the magnitude of emf induced in the coil while the current in the solenoid is changing?
1 Answers
Initially, magnetic flux passing through the coil (one turn), `phi_(1)=B.A=BA cos0^(@)`.
Magetic field at a point inside the solenoid is given by `B=mu_(0)nI`, where n is number of turns per metre,
`therefore" "phi_(1)nIxx(pid^(2))/(4)`
Here, n = 10000 turns per metre,
`I=1A,d=3.1cm`
`therefore" "phi_(1)=mu_(0)nI(pid^(2))/(4)=4pixx10^(-7)xx1xx10000xxpixx((3.1xx10^(-2))^(2))/(4)`
`=0.947xx10^(-5)Wb`
Finally, the flux becomes zero because the current reduces to zero.
Thus, induced emf, `e=(|Deltaphi|)/(Deltat)=(0.947xx10^(-5))/(10xx10^(-3))=9.47xx10^(-4)V`
The total emf =`Nxxe=60xx9.47xx10^(-4)=568.2xx10^(-4)V`