A very long solenoid of radius R  is carrying current  I(t)=kte^{-at}(k>0) as a function of time (t\geq 0). Counter clockwise current is taken to be positive . A circular conducting coil of radius 2R is place in a equatorial plane of the solenoid and concentric with the solenoid . The current induced in the outer coil is correctly depicted , as a function of time, by :

  • Option 1)

  • Option 2)

  • Option 3)

  • Option 4)

 

Answers (1)

Given,

I(t)=kte^{-\alpha t}

\phi=(\mu_0NI)A=\mu_0NKte^{-\alpha t}A

 indused current

I_(indused)=-\frac{d\phi}{dt}\times\frac{1}{R}

=-\mu_0NK[e^{-\alpha t}-\alpha t e^{-\alpha t}]

=-Ce^{-\alpha t}(1-\alpha t)

 

 


Option 1)

Option 2)

Option 3)

Option 4)

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