A dipole that carries charges \(\pm q\) is aligned along the \(y\) axis of an \(x y z\) rectangular coordinate system, with the midpoint of the dipole at the origin.

(a) Use Gauss's law to calculate the electric flux through the \(x z\) plane, which bisects the dipole and is perpendicular to the dipole moment. (Calculate the electric flux for each charge separately and apply the principle of superposition.)

(b) Calculate the flux through the \(x z\) plane by integrating the electric field in Eq. 23. 8 over the plane. (You'll need to generalize Eq. 23. 8 to any point on the \(x z\) plane by making the substitution \(x^{2} \rightarrow r^{2}=\left(x^{2}+z^{2}\right)\).)

(c) Which of the two techniques lets you obtain the flux through the \(x z\) plane more easily?

Data from Eq. 23. 8

Transcribed Image Text:

= = Ey Ey+Ey-(E++E_)cos d/2 =-(2k +32 + (8/2)) ((x + (2/2)11/2) =-k 9pd [x+(d/2)213/2