1.

A solenoid of resistance R and inductance L has a piece of soft iron inside it. A battery of emf E and of negligible internal resistance is connected across the solenoid as shown in Fig. At any instant, the piece of soft iron is pulled out suddenly so that inductance of the solenoid decrease to etaL(eta lt 1) with battery remaining connected. The work done to pull out the soft iron piece is

Answer»

`(eta LE^(2))/(2R^(2))`
`((1-eta)LE^(2))/(2R^(2))`
`((1-eta)LE^(2))/(etaR^(2))`
`((1-eta)LE^(2))/(2etaR^(2))`

Solution :`L_(1)=L, L_(2)=etaL, phi=L_(1)I_(1)=L_(2)I_(2)I_(1)=E//R`
`IMPLIES I_(2)=(L_1)/(L_2)I_(1)=I_(1)//eta`
`W=U_(f)-U_(i)=1/2 L_(2)I_(2)^(2)-1/2L_(1)I_(1)^(2)`
`1/2etaL((I_1)/(eta))^(2)-1/2 LI_(1)^(2)=(LE^2)/(2etaR^(2))[1-eta]`.


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