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Electricity and Magnetism

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Moderate

Construction Energy of a System of Two Arbitrarily Placed Charges

EANDM-FRONS0

Figure 1 depicts a system of two charges, in which charge $q_1$ lies along the positive $x$-axis, at a distance of $r_1 = 2.50 \text{ cm}$ from the origin.

Figure 1. “Timothy Black. Created for Albert.io. Copyright 2016. All rights reserved.”

Charge $q_2$ lies at a distance $r_2 = 1.50 \text{ cm}$ from the origin, along a line which makes an angle of $\theta_2 = 230^\circ$ with respect to the positive $x$-axis.

Let $q_1 = 0.64 \; \mu \rm{C}$ and $q_2 = 1.28 \; \mu \rm{C}$.

What energy $U$ is required to construct this system, assuming that the potential energy of the system is zero when all charges are infinitely separated?

A

$U = 4.62 \times 10^4 \text{ J}$

B

$U = 4.58 \times 10^7 \text{ J}$

C

$U = 5.53 \text{ J}$

D

$U = 0.202 \text{ J}$