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in Electrostatics by (15 points)
2. charges placed at a distance are in air exert a force f on each other value of distance R at which the experience force 4 F when they placed in medium dielectric constant K is equal to 60

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1 Answer

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by (15 points)
The force between two charges in a medium is given by Coulomb's law modified for the medium:


\[ F' = \frac{1}{4\pi \varepsilon\cdot K} \cdot \frac{q_1 \cdot q_2}{r^2}, \]


where \( F' \) is the force in the medium, \( \varepsilon \) is the permittivity of the medium, \( q_1 \) and \( q_2 \) are the charges, and \( r \) is the separation distance.


Since \( F' = 4F \) in this case, you can set up the equation:


\[ 4F = \frac{1}{4\pi \varepsilon\cdot 60} \cdot \frac{q_1 \cdot q_2}{R^2}, \]


where \( R \) is the new separation distance in the medium.


Solving for \( R \):


\[ R = \sqrt{\frac{q_1 \cdot q_2}{60\varepsilon\pi F}}. \]


Please provide the values of the charges (\( q_1 \) and \( q_2 \)) to calculate the distance \( R \).

Let \(F) be the force when charges was in air.


\[ F = \frac{1}{4\pi \varepsilon} \cdot \frac{q_1 \cdot q_2}{R^2}, \]

\[\{frac{F'}{F}} = \frac{60\cdot\(R)}{r}]

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