ELECTROMAGNETISM & RELATIVITY - Chapter 2, Exercise 2 Solution
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Electric Potential Energy from Charge and Potential

PROBLEM
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A +3 uC charge is placed at a point where the electric potential is
150,000 V. Calculate its electric potential energy at that location.

SOLUTION
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Using the electric potential energy formula:

    U = q V

Substitute the given values:

    q = 3 x 10^-6 C
    V = 150,000 V

    U = (3 x 10^-6) x 150,000
    U = 0.45 J

ANSWER: The charge's electric potential energy at that location is
0.45 J.

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WHY THIS WORKS AS AN ANSWER

Electric potential (V) is defined as potential energy PER UNIT
charge, so multiplying it by the actual amount of charge present (q)
directly recovers the total potential energy stored - the same
structural relationship as PE = mgh in Course 1, where gravitational
potential (gh) gets multiplied by the actual mass present to give
total potential energy. Because both the charge and the potential are
positive here, the potential energy is positive too, meaning the
charge would gain kinetic energy (per Course 1's own conservation of
energy) if released and allowed to move away toward a region of lower
potential.