ELECTROMAGNETISM & RELATIVITY - Chapter 2, Exercise 1 Solution
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Electric Field from a Point Charge

PROBLEM
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Calculate the electric field 0.5 m from a +8 uC point charge.

SOLUTION
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Using the electric field formula for a point charge:

    E = k Q / r^2

Substitute the given values:

    k = 8.99 x 10^9 N.m^2.C^-2
    Q = 8 x 10^-6 C
    r = 0.5 m

    E = (8.99 x 10^9) x (8 x 10^-6) / (0.5)^2
    E = 71,920 / 0.25
    E = 287,680 N/C (approximately 2.88 x 10^5 N/C)

ANSWER: The electric field 0.5 m from the charge is approximately
2.88 x 10^5 N/C, pointing directly away from the charge (since the
source charge is positive).

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WHY THIS WORKS AS AN ANSWER

The electric field formula, E = kQ/r^2, is Coulomb's law from Chapter
1 with the second charge (the "test charge" that would feel the
force) already divided out - it describes the field the source charge
alone creates at that point in space, independent of whether anything
is actually there to feel it. Because the source charge is positive,
the field points radially outward, away from the charge, matching the
direction a positive test charge would actually be pushed if placed
at that location.