Effective capacitance of a pair of media

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The discussion revolves around calculating the force of repulsion between two identical point charges with a dielectric slab inserted between them. Two methods are used: one calculates the effective distance using the dielectric constant, yielding a force of 4/9 * F, while the other determines effective capacitance for the two media, resulting in 5/8 * F. The discrepancy in results raises questions about the correctness of the methods applied. Participants are examining the assumptions and formulas used in each approach to identify potential flaws. Clarifying the principles of electrostatics and dielectric effects is crucial for resolving the differences in outcomes.
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The force of repulsion between two identical point charges when kept with a separation r in air is F. Half the gap between the two charges is filled by a dielectric slab of dielectric constant K=4. What is the new force of repulsion between the two charges?
This is the question.

Now if I solve it by finding effective distance between the two charges(using the formula r(effective) =r sqrt(K)) ... I get answer as 4/9 *F.

But if I solve by finding effective capacitance of the two media (by applying formula for capacitors in series and finding effective capacitance by using K=C'/C).. I get the answer as 5/8 *F

Why am I getting different answers? Is there some flaw in my methods?
 
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