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To calculate the force of interaction between two charges in a medium other than vacuum, we can use Coulomb’s Law, modified to account for the dielectric constant of the medium ((epsilon_r)).
The formula for the force between two point charges in a vacuum is given by Coulomb’s law as:
[
F = k frac{{|q_1 q_2|}}{{r^2}}
]
where
– (F) is the force between the charges,
– (q_1) and (q_2) are the magnitudes of the two charges,
– (r) is the distance between the charges, and
– (k) is Coulomb’s constant. For calculations in the cgs system (centimeter, gram, second), specifically for charges measured in statcoulombs, (k) is set to 1 in the appropriate units, which simplifies the equation to:
[
F = frac{{|q_1 q_2|}}{{r^2}}
]
When considering a medium with a dielectric constant (epsilon_r), the force is reduced compared to the force in a vacuum. The modified Coulomb’s law takes the dielectric constant into account:
[
F = frac{{1}}{{4 pi epsilon_0 epsilon_r}} frac{{|q_1 q_2|}}{{r^2}}
]
In the cgs system, (4 pi
d
Explanation: 1 stat coulomb = 1/(3 X 109
) C
F = (1.998 X 1.2488 X 10-16)/(4∏ X 8.854 X 10-12 X 2.2 X (7.5 X 10-2
)
2
) = 1.815 X 10-4 N