Like Charges and the Electric Quadrupole

Theory

By the superposition principle, the total field is the vector sum $\vec{E}=\sum k{q}_i{\hat{r}}_i/r_i^2$. Between two like charges there is a neutral point where $\vec{E}=0$. Four alternating charges form a quadrupole, whose field falls off as $1/r^4$ far away.

What to observe

• Left: lines from two positive charges repel each other; the midpoint is neutral.
• Right: the quadrupole’s lines close between neighbouring charges.

Try this

• Switch to Electric potential to see the saddle point.
• Move one charge of the quadrupole and break the symmetry.

Also available in: Cargas iguais e quadrupolo elétrico (Português) · Cargas iguales y cuadrupolo eléctrico (Español)