Three particles lie on the x axis: particle 1, with a charge of 1 * 10^-⁸ C is at x = 1 cm, particle 2, with a charge of 2 *10^-⁸ Cis at x = 2 cm, and particle 3, with a charge of -3 *10^-⁸ C, is at x = 3 cm. The potential energy of this arrangement, relative to the potential energy for infinite separation, is:

Question

Quizplus · Accepted Answer

The potential energy of this system, relative to infinite separation, is given by the equation:

$$U = \frac{1}{4\pi\epsilon_0}\left(\frac{q_1 q_2}{r_{12}} + \frac{q_1 q_3}{r_{13}} + \frac{q_2 q_3}{r_{23}} ight) - \frac{1}{4\pi\epsilon_0}\left(\frac{q_1 q_2}{r_{\infty}} + \frac{q_1 q_3}{r_{\infty}} + \frac{q_2 q_3}{r_{\infty}} ight)$$

where $r_{ij}$ is the distance between particles $i$ and $j$, and $r_{\infty}$ is the separation between particles when they are infinitely far apart.

Plugging in the values, we get:

$$U = \frac{1}{4\pi\epsilon_0}\left(\frac{(1)(2)}{0.01} + \frac{(1)(-1)}{0.02} + \frac{(2)(-1)}{0.01} ight) - \frac{1}{4\pi\epsilon_0}\left(\frac{(1)(2)}{\infty} + \frac{(1)(-1)}{\infty} + \frac{(2)(-1)}{\infty} ight)$$

Simplifying, we get:

$$U = -4.9	imes10^{-19} 	extrm{ J}$$

Relative to the potential energy for infinite separation, the answer is  $-4.9$J. Thus, the best choice is B.

Three Particles Lie on the X Axis: Particle 1, with a Charge