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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 why is this wrong???

8 years ago

Answers : (2)

Chetan Mandayam Nayakar
312 Points

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

8 years ago
Aishwarya Prem Renu
18 Points

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

7 years ago
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