For a conservative electric force, how is \(\Delta U\) related to the work \(W_{\mathrm{elec}}\) done by the electric force?

If the electric force does \(+6.0\,\mathrm{J}\) of work, what is \(\Delta U\)?

With \(U(\infty)=0\), is the potential energy of two like point charges positive or negative?

Find \(U\) for charges \(+3.0\,\mathrm{nC}\) and \(+4.0\,\mathrm{nC}\) separated by \(0.20\,\mathrm{m}\).

Find \(U\) for charges \(+2.0\,\mathrm{nC}\) and \(-5.0\,\mathrm{nC}\) separated by \(0.50\,\mathrm{m}\).

An external agent slowly brings two like charges from infinity to separation \(r\). Is the external work positive, negative, or zero? Explain the sign.

Two charges are released from rest and their electric potential energy decreases by \(2.4\,\mu\mathrm{J}\). If no other force does work, find the change in total kinetic energy.

A pair of charges changes separation from \(r_i\) to \(r_f\). Derive \(\Delta U\) in terms of \(q_1,q_2,r_i,r_f\).

Three point charges \(q_1,q_2,q_3\) are fixed at the corners of a triangle with side separations \(r_{12},r_{13},r_{23}\). Derive the total electric potential energy of the arrangement and state why there is no single-charge term.

Two like charges \(q\) and \(Q\) are released from rest at separation \(r_0\). Treating them as isolated point charges, derive the total kinetic energy when their separation is \(r>r_0\), and state the limiting total kinetic energy as \(r\to\infty\).