QuestionThe potential energy of a system of three equal charges arranged in an equilateral triangle is 0.54 J If the length of one side of this triangle is 33 cm , What is the charge of one of the three charges? (a) $\quad 1.7 \mu \mathrm{C}$ (b) $4.3 \mu \mathrm{C}$ (C) $\quad 2.6 \mu \mathrm{C}$ (d) $\quad 2.0 \mu \mathrm{C}$

Studdy Solution
Solve for the charge $q$.
First, simplify the equation:
$$0.54 = \frac{26.97 \times 10^9 \cdot q^2}{0.33}$$
Multiply both sides by 0.33 to isolate the term with $q^2$:
$$0.54 \times 0.33 = 26.97 \times 10^9 \cdot q^2$$
$$0.1782 = 26.97 \times 10^9 \cdot q^2$$
Divide both sides by $26.97 \times 10^9$:
$$q^2 = \frac{0.1782}{26.97 \times 10^9}$$
$$q^2 = 6.61 \times 10^{-12}$$
Take the square root of both sides to solve for $q$:
$$q = \sqrt{6.61 \times 10^{-12}}$$
$$q \approx 2.57 \times 10^{-6} \, \mathrm{C}$$
Convert to microcoulombs ($\mu \mathrm{C}$):
$$q \approx 2.57 \, \mu \mathrm{C}$$
The closest option is:
(c) $2.6 \, \mu \mathrm{C}$