What is the electric field magnitude a distance \(r\) from a point charge \(Q\)?

Does the field from a positive point charge point toward or away from the charge?

At a point \(0.50\,\mathrm{m}\) from a negative point charge, what is the direction of that charge's field contribution?

Find the field magnitude \(0.20\,\mathrm{m}\) from a \(+8.0\,\mathrm{nC}\) point charge.

A point charge produces field magnitude \(E\) at radius \(r\). What field magnitude does it produce at radius \(2r\)?

Two equal positive charges are placed at \(x=\pm0.30\,\mathrm{m}\). What is the net electric field at the origin?

Charges \(+5.0\,\mathrm{nC}\) and \(-5.0\,\mathrm{nC}\) are at \(x=-0.20\,\mathrm{m}\) and \(x=+0.20\,\mathrm{m}\). Find the electric field at the origin.

A charge \(+Q\) is at the origin. Derive the electric field vector at position \((x,y)\).

A uniformly charged thin rod of length \(L\) lies on the \(x\)-axis from \(-L/2\) to \(+L/2\). At point \((0,a)\), identify which field components cancel by symmetry and write the remaining component as an integral.

Two charges \(+Q\) at \(x=-a\) and \(-\alpha Q\) at \(x=+a\), with \(\alpha>0\), create a field at the origin. Derive \(\vec E(0)\), then find the value of \(\alpha\) that makes the field magnitude equal to the field from a single \(+Q\) charge at distance \(a\).