**Goal:** Reason with electric fields

**Source:** 283-370 E due to circular rods

All of the curved charged rods shown in the image below have the same

radius and linear charge density (though some are positively charged and

others are negatively charged). For which configuration would the

magnitude of E at the origin be greatest?

## Commentary:

## Answer

(6) This problem constitutes a good exercise for students learning the

vector nature of the electric field. There are many good followup

questions, such as; Which configurations have zero field at the origin?,

Order the configurations by increasing magnitude of electric field at

the origin. Stress the value of symmetry for reasoning to the answer. A

negative distribution in a quadrant is equivalent to a positive

distribution in the opposite quadrant, which means that distributions #5

and #7 are equivalent (for purposes of finding the E field at the

origin).