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  • Coulomb's Law: Calculating the Force Ratio Between Two Charges
    To have the ratio of force acting on 2 charges 1 and 5 will be 11, the charges should be 1 and 25.

    The force between two charges is given by Coulomb's law:

    $$F = k\frac{q_1q_2}{r^2}$$

    where k is a constant, q1 and q2 are the charges, and r is the distance between the charges.

    So the force acting on 2 charges 1 and 5 will be:

    $$F1 = k\frac{1\cdot1}{r^2}$$

    The force acting on 2 charges 1 and 25 will be:

    $$F2 = k\frac{1\cdot25}{r^2}$$

    Therefore the ratio of the force will be:

    $$\frac{F1}{F2}=\frac{1/r^2}{25/r^2}=\frac{1}{25}$$

    In order for the ratio to be 11, we can have 11 charges on one side and 25 on the other side.

    Then the ratio will be:

    $$\frac{F11}{F25}=\frac{11/r^2}{25/r^2}=\frac{11}{25}$$

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