Problem: A dipole lies on the x-axis, with the positive charge on x = d/2 and the negative charge on x = -d/2. Find the electric flux through the yz plane midway between the charges.

Solution:

To find the electric flux through the yz plane, we can use Gauss's law, which states that the electric flux through a closed surface is proportional to the enclosed charge. We can imagine a spherical surface centered on the midpoint of the dipole, with radius r. The electric flux through this surface will be the same as the flux through the yz plane, since they both enclose the same charge.

1. Calculate the Electric Field Due to the Dipole:
To find the electric field due to the dipole, we can use the equation:
E = (1/4πε0) * ((2p)/(r^3))
where p is the dipole moment, which is equal to qd, where q is the charge on each end of the dipole and d is the distance between them.

2. Determine the Flux:
The flux through the spherical surface is given by:
ΦE = E * A
where A is the surface area of the sphere. Since the sphere is centered on the midpoint of the dipole, the electric field will be perpendicular to the surface at all points, so the flux will be the same at every point on the surface.

3. Calculate the Enclosed Charge:
The enclosed charge is equal to the sum of the charges on the two ends of the dipole, which is zero. Therefore, the electric flux through the yz plane midway between the charges is zero.

Conclusion: The electric flux through the yz plane midway between the charges is zero because the enclosed charge is zero.

2×(2Qπk)=(4Qπk).. draw field lines and you will find that half of the field lines of +ve
charge pass through y-z plane so..flux of +ve charge through y-z axis is (2Qπk).. similarly for -ve charge. Is it helpful