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There are two capacitor plates and two different dielectric media are filled in such a way that one side of the diagonal is filled with dielectric medium with constant k1 and the other side with a constant k2. This is an IITJEE question and the soln gives the answer as eA( k1*k2) (ln( k1)-ln(k2))/ d( k1-k2) But if we substitute k1=k2=k, we get the result as an indeterminate form which doesn't make sense. Instead, why can't we divide it into 4 parts equal ( 2 lines thru the middle along length and breadth) in such a way that two diagonally opp parts have capacitance identical to that of the full capacitor and the other two parts are either fully filled with k1 or with k2.? doing it in that method, the answer comes as eA (k1k2)^0.5 / d. Here applying the boundary condn k1=k2=k also works..so why is this wrong???

There are two capacitor plates and two different dielectric media are filled in such a way that one side of the diagonal is filled with dielectric medium with constant k1 and the other side with a constant k2. This is an IITJEE question and the soln gives the answer as


eA( k1*k2) (ln( k1)-ln(k2))/ d( k1-k2)


But if we substitute k1=k2=k, we get the result as an indeterminate form which doesn't make sense.


Instead, why can't we divide it into 4 parts equal ( 2 lines thru the middle along length and breadth) in such a way that two diagonally opp parts have capacitance identical to that of the full capacitor and the other two parts are either fully filled with k1 or with k2.?


doing it in that method, the answer comes as


eA (k1k2)^0.5 / d.


Here applying the boundary condn k1=k2=k also works..so why is this wrong???

Grade:

2 Answers

Chetan Mandayam Nayakar
312 Points
9 years ago

If you encounter an indeterminate form, then use L Hospitals Rule

Aishwarya Prem Renu
18 Points
8 years ago

This is a physics problem. In capacitors! Nothing to do with limits! 

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