Does a grounded conductor have zero charge? If a charged conductor is connected to ground, does that mean that along with the potential of the conductor being zero, the charge on it is also zero as soon as it is connected to ground?
 A: Grounding a conductor just means setting its voltage to $0$.
One assumes the ground is an "infinite" reservoir of charge. Grounding a conductor means that now charge can flow in/out of the reservoir so that the final charge $Q_c$ on the conductor is such that its voltage is 0.
This final value $Q_c$ is not necessarily 0!
Let's do a quick example.
Assume you have a hollow thin spherical conductor, with initially no net charge, with a charge $q$ inside. This will lead to a charge $q_-=-q$ on the inner shell of the conductor and a charge $q_+=q$ on the outer shell, so that the total charge on the conductor is $Q_c=q_-+q_+=0$.
Using Gauss law, we can compute the voltage of the conductor by taking a spherical virtual surface of radius $r$ (bigger than the conductor's radio) and that leads to $V(r)=q_{in}/4\pi\epsilon_0 r$ where $q_{in}=q$ is the total charge inside the virtual surface.
If one now grounds the conductor's outer shell, some charge will flow on/from the outer shell, using the infinite reservoir of charge, so that one gets $V(r)=0$ i.e. $q_{in}=0$. Because
$$q_{in}=q+q_-+q_+$$ and we cannot remove the charge in the middle $q$, this means that the total charge on the conductor now is $Q_c=q_-+q_+=-q$.
Briefly, what happened is that the ourside charge vanished and only the charge $q_-=-q$ on the inside shell stayed. But the final effect is that from an initial condition of $Q_c=0$ we end up to the final condition $Q_c=-q$ i.e. the conductor actually acquired some charge $-q$!
So you see, grounding means setting $V=0$ but not necessarily $Q_c=0$!
(By the way, this is how a Faraday cage works)
Of course, we could do the same reasoning with a conductor having an initial charge $Q_0$ and that would lead to a final charge of $Q_0-q$, so this also holds for conductor with an initial charge.
A: Not necessarily. For example, if there is another nearby charge, the conductor may need to gain charges so as to nullify its potential.
A: A grounded conductor has the potential of the ground which is assumed to be zero.
But it does not imply that charge will also be zero on this conductor.
A: When we only consider a single charged conductor(isolated) then it becomes electrically neutral on earthing. But if the charged conductor is in the influence of another charged body then the potential near the conductor will change and will be dependent on both the charged bodies (principle of superposition ). So the amount of charge that flowed into the earth will not be the same as in the former case. Eg - When a conductor has -5C charge and it is earthed the conductor becomes electrically neutral as all the negative charge flows from the conductor to the earth till the potential difference becomes zero (since in this case the P.D was due to the -5C charge only so all of the charge flows). If another charged body is placed near this -5C charged conductor then the potential near the latter changes (increases or decreases depending on the nature of the charge placed). This time more or less charge might be required to flow into the earth depending increase or decrease in potential.
Note : Just in case you didn't know , charge only flows when there is a potential difference and also the magnitude of charge flowing also depends on the P.D (Ohm's law - $V=RI$, i.e. $I=\frac{V}{R}$ )
