A dipole is located at the origin, with charges + 3 nC and - 3 nCseparated by 4 μm. Consider a spherical Gaussian surfacecentered on the origin of radius 80 μm.

a) What is the electric flux through the Gaussiansurface?

b) Now suppose you have a Gaussian sphere of radius1 μm centered on the positive charge. What is the fluxthrough this Gaussian surface?

a)

The Gaussian surface must have contained both the charges like + 3 nC and - 3 nC, total charges being zero. According the Gauss's law, total electric flux over a closed surface is equal to 1 / ε₀ times the total charge contained inside the closed surface.

Since total charge inside is zero, total flux will be 1 / ε₀ x 0 = 0

b)

In this case the Gaussian surface is so small that it contains only the charge

+ 3 nC.

So electric flux over the Gaussian surface

= (1 / ε₀) x 3 x 10⁻⁹

= (1 / 8.85 x 10⁻¹²) x 3 x 10⁻⁹

= 3 x 10³ / 8.85

= 339 weber.

=