Effective capacitance of a pair of media

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SUMMARY

The discussion centers on calculating the force of repulsion between two identical point charges with a dielectric slab inserted between them. The first method utilizes the effective distance formula, yielding a force of 4/9 * F, while the second method applies the effective capacitance formula for capacitors in series, resulting in a force of 5/8 * F. The discrepancy arises from the different approaches to modeling the system, highlighting the importance of consistency in method selection when dealing with dielectric materials.

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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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