Effective capacitance of a pair of media

In summary, the force of repulsion between two identical point charges in air at a separation of r is F. When a dielectric slab with a dielectric constant of K=4 fills half of the gap between the charges, the new force of repulsion is either 4/9 *F or 5/8 *F, depending on the method used to solve the problem. While one method involves finding the effective distance between the charges using the formula r(effective) =r sqrt(K), the other method involves finding the effective capacitance of the two media by applying the formula for capacitors in series and using K=C'/C. The discrepancy between the two answers may suggest a flaw in one of the methods.
  • #1
Prajwal
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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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Related to Effective capacitance of a pair of media

1. What is the definition of effective capacitance?

The effective capacitance of a pair of media is the combined capacitance of two or more capacitors that are connected in series or parallel.

2. How is effective capacitance calculated?

The effective capacitance can be calculated using the following formulas:- For capacitors connected in series: 1/Ceff = 1/C1 + 1/C2 + ...- For capacitors connected in parallel: Ceff = C1 + C2 + ...

3. What factors affect the effective capacitance?

The effective capacitance is affected by the type of material used for the capacitors, the distance between them, and the dielectric constant of the material between them.

4. Why is effective capacitance important?

Effective capacitance is important because it determines the amount of charge that can be stored in a given system of capacitors. It also affects the overall performance and efficiency of electronic circuits.

5. How can the effective capacitance be increased?

The effective capacitance can be increased by adding more capacitors in series or parallel, increasing the surface area of the capacitor plates, or using a dielectric material with a higher dielectric constant.

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