a) Calculate the magnitude of the electric field at point P with the superpositi

Question

a) Calculate the magnitude of the electric field at point P with the superposition principle.

b) 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.

Two charges, +q and -q, are located in the x-y plane at points (0,+d/2) and (0,-d/2), respectively. Data: q = 24.0 nC, d = 4.20 mm and P is at x = 84.0 mm. Calculate the magnitude of the electric field at point P with the superposition principle. 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.

Explanation / Answer

the electric field of a point charge q is given by

E=kq/r^2

at point x=84mm

electric field due to +q is

E=kq/(x-d/2)^2

and electric field due to point -q is

E=-kq/(x+d/2)^2

so net electric field=kq/(x-d/2)^2-kq/(x+d/2)^2

=kq(2xd/(x^2-d^2/4)^2)

E=3057.4N/c

b)electric field due to dipole is

E=kqd/x^3=1530.6N/C

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