Flux due to charge placed ON a sphere

Question

Question

If we place a charge, say Q, ON the surface of a sphere, will there be a flux through the sphere?

My Understanding of the Concept

I'm studying high school physics, so I have learnt Gauss's Law and according to it if a charge is placed inside the sphere, a flux is produced. And if the charge is placed outside the sphere, the net flux through the sphere is 0 as entering flux equals the leaving flux.

So while practicing a few workout exercises, I encountered this particular problem:

A uniformly charged conducting sphere of 2.4 m diameter has a surface charge density of 80 μC/m^2. So, what is the total electric flux leaving the surface of the sphere?

So over here I assumed the answer will be zero as the charged enclosed within the surface of the sphere is 0 so flux becomes 0 from the Gauss's formula that says flux=q(enclosed)/epsilon The reason due to which I assumed charge inside is 0 is because the question says surface charge density, which basically is (Net Charge)/Area, rather than volume charge density.

Please kindly help me with this

Answer 1

The problem statement asks for the net flux leaving the sphere, not through the sphere as you initially stated.

Therefore you would imagine a closed surface outside the sphere, e.g., another imaginary sphere. Then, per Gauss' law the net flux produced by the charged sphere across the surface of the imaginary sphere is

$$\phi=\frac{Q}{e}$$

where $Q$ is the net charge on the sphere and $\epsilon$ is the electrical permittivity of the space.

In this case

$$Q=\pi d^{2}\sigma$$

Where $d$ is the diameter of the charged sphere and $\sigma$ is the charge density on the sphere.

Hope this helps

Answer 2

If the charge is uniformly distributed on the surface of the sphere, place a spherical Gaussian anywhere outside the surface to get the outward flux (which will appear to be from a point charge).