Identical 8.0-μC point charges are positioned on the x axis at x = ±1.0 m and released from rest simultaneously. What is the kinetic energy of either of the charges after it has moved 2.0 m?
A) 84 mJ
B) 54 mJ
C) 96 mJ
D) 63 mJ
E) 48 mJ

Question

Quizplus · Accepted Answer

The initial potential energy between the two charges is calculated by:
$$U_i = \frac{1}{4\pi\epsilon_0}\cdot\frac{(8.0\ \mu C)^2}{2.0\ m} = 72	ext{ mJ}$$
As the charges move apart to a distance of 2.0 m, the potential energy is converted to kinetic energy, which is the same for both charges. Using conservation of energy:
$$U_i = K_f$$
$$\frac{1}{2}mv^2 = U_i = 72	ext{ mJ}$$
where $m$ is the mass of one charge and $v$ is its velocity after traveling 2.0 m. Solving for $v$ gives:
$$v = \sqrt{\frac{2U_i}{m}} = 8.49	imes 10^5	ext{ m/s}$$
The kinetic energy of one of the charges is then:
$$K_f = \frac{1}{2}m v^2 = 96	ext{ mJ}$$
Therefore, the answer is C.