Two charges, +q and -q, are located in the x-y plane at points (0,+d/2) and (0,-

Question

Two charges, +q and -q, are located in the x-y plane at points (0,+d/2) and (0,-d/2), respectively. Calculate the magnitude of the electric field at point P with the superposition principle.

Data: q = 23.0 nC, d = 4.60 mm and P is at x = 92.0 mm.

second part of the question:

In the previous problem, you can get an approximate answer for the electric field at point P by using the electric dipole approximation which is valid for the limit x>>d. Calculate the magnitude of the electric field at point P with this approximation and the same values for Q, d and x as in the previous problem.

Showing how to do the problem will be greatly appreciated.

Two charges, +q and -q, are located in the x-y plane at points (0,+d/2) and (0,-d/2), respectively. Calculate the magnitude of the electric field at point P with the superposition principle. Data: q = 23.0 nC, d = 4.60 mm and P is at x = 92.0 mm. second part of the question: In the previous problem, you can get an approximate answer for the electric field at point P by using the electric dipole approximation which is valid for the limit x>>d. Calculate the magnitude of the electric field at point P with this approximation and the same values for Q, d and x as in the previous problem. Showing how to do the problem will be greatly appreciated.

Explanation / Answer

a) E(+q) = k*q/r^2 = 9.0x10^9*29.0x10^-9/(0.056 - 0.00280/2)^2 = 8.75x10^4N/C (+x)

Now E(-q) = k*q/r^2 = 9.0x10^9*29.0x10^-9/(0.056 + 0.00280/2)^2 = 7.92x10^4N/C (-x)

So E net = 8.75x10^4N/C - 7.92x10^4N/C = 8333N/C (+x)


b) The approximation for E = 2*k*q*d/x^3 = 2*9.0x10^9*29.0x10^-9*2.8x10^-3/(0.056^3

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