View attachment 345350It represents the net field with a perpendicular component that cannot exist. If it did, it would have to rotate to new position when the charge distribution is rotated. The idea is simple. Look at figure (A) on the right. The lines of charge are colored to tell them apart but they have identical charge per unit length length ##\lambda.## If I rotate (A) by 120° about an axis that is perpendicular to the screen and connects point (3,3,3) with the origin, I get figure (B). The charge distribution in (B) is identical to (A). This means that the
net field everywhere in space in (B) must be identical to (A). The only way that the
net field can look the same before and after the rotation is if its perpendicular component is zero because this component rotates with the distribution while the component along the axis does Not.
