O ne positive (+2q) and two negative (%u2212q) charges are arranged as displayed

Question

One positive (+2q) and two negative (%u2212q) charges are arranged as displayed in figure 1. Calcu- late electric field E(y) and electric potential %u03C6(y) at points along positive y%u2212axis as a function of their coordinate y. What nonzero component(s) does E have? Does its y%u2212component Ey satisfy Ey = %u2212%u2202%u03C6/%u2202y? Is it supposed to satisfy?

Let us now look more closely at how the magnitude of the electric field E(y) falls off with distance y far away from this system of charges. As an example, calculate the numerical value of the ratio E(y = 10a)/E(y = 20a). We know that the doubling of the distance from a single point charge would result in the field decreasing by a factor of 22 = 4. The electric field of an electric dipole would decrease by a factor of 23 = 8. What is the (approximate) power n in 2n that you find for our system in this numerical example? (That would translate in the scaling E(y %u226B a) %u221D 1/yn for our system.) Any comments on your finding?

Explanation / Answer

Hopefully, that clarify things...I thought I put the figureup. Hope you guys have much more success with this questionthan I did....

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