What happens if a positive charge and a negative charge meet? If charge cannot be created or destroyed, then how do charges neutralise each other? do they both just become uncharged particles?
 A: In electrostatics, When someone says that the body is neutral means that the body has an equal amount of positive and negative charges. So that net charge
$$Q_{net}=\int \rho dV=0$$
It doesn't mean that charges get annihilate or something.
You might argue that if there is a charge in the body, then there should be an electric field. The answer is Yes! A neutral body produces electric fields.
If you do a multipole expansion of the potential, then you find
$$\phi=\frac{1}{4\pi \epsilon_0}\left[\frac{K_0}{r}+\frac{K_1}{r^2}+\frac{K_2}{r^3}+\cdots\right]$$
The behavior of the potential at
large distances from the source will be dominated by the first term in the
above series whose coefficient is not zero.
First-term $K_0$ is the total charge on the body which is zero for a neutral body. The second term $K_1$ is known as a dipole moment. If there is a dipole moment in the body then it will produce an electric field.
In ordinary cases, there is no dipole moment unless the external field is applied to a body.


If the charge cannot be created or destroyed, then how do charges neutralize each other?

In particle physics, annihilation is the process that occurs when a subatomic particle collides with its respective antiparticle to produce other particles, such as an electron colliding with a positron to produce two photons.
It's not a violation of charge conservation.
A: "Charge" can be created or destroyed, locally. The net charge of a system is what is conserved: it has the same value before and after any transformation. For example, using two high-energy photons, an electron can be produced in some place, "creating" negative charge there, so long as a positron is produced nearby, such that the overall charge of all particles involved (photons, then electron and positron) has not changed (0=-1+1).
