Adipole that carries charges ±q is aligned along the y axis of an xyz rectangular coordinate system, with the midpoint of the dipole at the origin.

a) use gauss's law to calculate the electric flux through the xz plane, which bisects the dipole and is perpendicular to the dipole moment. (hint: calculate the electric flux for each charge separately and apply the principle of superposition.)

express your answer in terms of q and the permittivity constant ϵ0.

b) calculate the flux through the xz plane by integrating the electric field in the equation e⊥=ey=−kqpd(x2+(d/2)2)3/2 over the plane. (you'll need to generalize in the equation to any point on the xz plane by making the substitution x2→r2=(x2+

express your answer in terms of q and the permittivity constant ϵ0.