Two like charges are near each other. Is the electric force attractive or repulsive?

If the distance between two point charges doubles, by what factor does the force magnitude change?

Two charges are \(-2q\) and \(+3q\). Is \(q_1q_2\) positive or negative, and what does that imply about attraction or repulsion?

Find the force magnitude between \(+4.0\,\mathrm{nC}\) and \(+6.0\,\mathrm{nC}\) separated by \(0.30\,\mathrm{m}\).

Two charges exert a force of \(2.0\,\mathrm{mN}\) at separation \(r\). What is the force magnitude at separation \(3r\), with charges unchanged?

Charge \(q_1=+5.0\,\mathrm{nC}\) is at \(x=0\), and \(q_2=-2.0\,\mathrm{nC}\) is at \(x=0.40\,\mathrm{m}\). Find the direction of the force on \(q_2\).

Charges \(+3.0\,\mathrm{nC}\), \(-3.0\,\mathrm{nC}\), and \(+1.0\,\mathrm{nC}\) lie on the \(x\)-axis at \(x=-0.20\,\mathrm{m}\), \(x=+0.20\,\mathrm{m}\), and \(x=0\). Find the net force on the middle charge.

Two equal positive charges are fixed at \((\pm a,0)\). A positive test charge is at \((0,b)\). Derive the direction of the net force on the test charge by symmetry.

Three charges lie on a line: \(+Q\) at \(x=-a\), \(+4Q\) at \(x=+a\), and a charge \(q\) somewhere between them. Find the position where the net force on \(q\) is zero, and state why the answer is independent of \(q\).

Two fixed charges \(Q_1\) at \(x=0\) and \(Q_2\) at \(x=L\) have the same sign but unequal magnitudes. Derive the condition for a zero-force point between them, and explain why no between-the-charges zero exists if their signs are opposite.