Does a Charged Rod Repel More Strongly Than a Point Charge?

[jcfor3ver]

HELP PLEASE! A pt charge question.

Homework Statement

Would a rod with +2Q charge repel a +q charge (placed a distance d from the center of the rod) more than a +2Q point charge repelling a +q charge (same distance away as the rod charge) ?

Homework Equations

Eforce=k(q1)(q2)/d^2

Efield of rod = (1/4pi*(epsilonsubnot which = 8.85*10^-12))* (magnitude of q/d*sqrt(d^2+(L/2)^2))

The Attempt at a Solution

I would think so since the rod is acting on the point charge in both y and x components.

Also, would the same rod from above, repel the same +q charge more than an arced rod with the same scenario (equidistant d from the center)?

 

[AlexChandler]

I would think about it like this.
Think of the rod as made of tiny point charges. When you make a vector sum of all of the force contributions made by all of the point charges, won't some parts of the contributions cancel? Think about the components of the force vectors that are parallel to the rod.

In the case of two point charges, there will be no canceling.

 

[kuruman]

Let's reason this out. Consider point charges +2Q and +q separated by d. The force on +q is F₀=k(2Q)q/d². Now divide +2Q in two equal pieces and place them a distance x apart so that +q is on the perpendicular bisector of x.

Is the resultant force on +q greater than, equal to or smaller than F₀?