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1. The problem statement, all variables and given/known data

For the electric dipole shown in the figure, express the magnitude of the resulting electric field as a function of the perpendicular distance x from the center of the dipole axis in terms of the electric dipole moment, p.

2. Relevant equations

E = Fq

P = qd

E = kq/(r^2)

3. The attempt at a solution

R = sqrt[(d/2)^2 + x^2]

q = P/d

Thus,

E = kP/{d*[sqrt(d/2)^2+x^2]^2}

Since I'm looking for the x-component, multiply E by the cos(theta), which in this case is x/R, or...

cos(theta) = x/sqrt[(d/2)^2+x^2]

so the answer i get is....

E = kP/{d*[sqrt(d/2)^2+x^2]^2} * x/sqrt[(d/2)^2+x^2]

which comes out to be...

E = kP/[sqrt(d/2)^2+x^2]^(3/2) * x/d

The final answer is actually...

E = kP/[sqrt(d/2)^2+x^2]^(3/2)

So my question is, what happens to the x/d?

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# Electric Dipole Electric Field

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