What is the electric potential from a point charge \(Q\) at distance \(r\), using \(V(\infty)=0\)?

When adding electric potentials from several point charges, do you add scalars or vector components?

At equal distance from charges \(+Q\) and \(-Q\), what is the net electric potential?

Find the potential \(0.40\,\mathrm{m}\) from a \(+5.0\,\mathrm{nC}\) charge.

Charges \(+3.0\,\mathrm{nC}\) and \(-1.0\,\mathrm{nC}\) are both \(0.20\,\mathrm{m}\) from point P. Find \(V_P\).

Two charges \(+Q\) are at \(x=\pm a\). Find the potential at the origin.

Two charges \(+Q\) and \(-Q\) are at \(x=-a\) and \(x=+a\). At the origin, compare the electric potential and electric field qualitatively.

A uniformly charged ring has total charge \(Q\) and radius \(R\). Derive the potential at a point on its axis a distance \(x\) from the center.

A uniform line charge with density \(\lambda\) lies on the \(x\)-axis from \(0\) to \(L\). Derive an integral expression for the potential at point \(x=a>L\), then evaluate it.

Charges \(+Q\) at \(x=-a\) and \(-\alpha Q\) at \(x=+a\) create potential at the origin. Derive \(V(0)\), find \(\alpha\) for which \(V(0)=0\), and explain whether the electric field at the origin is also zero for that \(\alpha\).