A doorknob carries a charge q1 = -1.5 nC, treated as concentrated at its center. A speck of dust carrying q2 = 0.20 nC sits 3.5 cm from that center. Using U_E = k q1 q2 / r, what is the electric potential energy of this doorknob-dust pair?

1. U_E = k q1 q2 / r = (8.99 x 10^9 N m^2/C^2)(-1.5 x 10^-9 C)(2.0 x 10^-10 C) / (0.035 m). 2. The numerator works out to -2.7 x 10^-9 N m^2 C^-1, and dividing by 0.035 m gives -7.7 x 10^-8 J. 3. The charges have opposite signs, so this potential energy is negative, meaning the pair attracts and would release energy if allowed to come together. 4. Option C keeps the correct size but drops the negative sign, missing that opposite-sign charges always give a negative potential energy, which is the sign trap for attracting pairs of charges. _Source: OpenStax Physics (CC BY 4.0), Ch 18 "Static Electricity", section 18.4 Electric Potential_