ELECTROMAGNETISM & RELATIVITY - Chapter 1, Exercise 1 Solution
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Force Between Two Opposite Charges (Coulomb's Law)

PROBLEM
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Two point charges, +5 uC and -4 uC, are separated by 0.3 m. Calculate
the magnitude of the force between them, and state whether the force
is attractive or repulsive.

SOLUTION
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Using Coulomb's law:

    F = k q1 q2 / r^2

Substitute the given values (using magnitudes for the force
calculation):

    k = 8.99 x 10^9 N.m^2.C^-2
    q1 = 5 x 10^-6 C
    q2 = 4 x 10^-6 C
    r = 0.3 m

    F = (8.99 x 10^9) x (5 x 10^-6) x (4 x 10^-6) / (0.3)^2
    F = (8.99 x 10^9) x (2 x 10^-11) / 0.09
    F = 0.1798 / 0.09
    F = 1.998 N (approximately 2.0 N)

ANSWER: The magnitude of the force is approximately 2.0 N. Since the
two charges have OPPOSITE signs (+5 uC and -4 uC), the force is
ATTRACTIVE - each charge pulls the other toward it.

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WHY THIS WORKS AS AN ANSWER

Coulomb's law formula uses the magnitudes of the two charges to find
the SIZE of the force; the SIGNS of the charges separately determine
its direction, exactly as the chapter's own text states - like
charges (both positive or both negative) repel, while unlike charges
(one positive, one negative, as in this problem) attract. This mirrors
the two-part answer structure every Coulomb's law problem needs: a
magnitude from the formula, and a direction reasoned separately from
the signs involved.