Electric charge is used to describe the behavior of electrons which seek to counterbalance the positive charge of protons.
But I have read about other forces which also attract electrons to atoms, could someone explain the mechanism behind electronegativity? Or why an electron might seek to enter the orbit of an atom which was already electrically neutral?
The short answer is: electromagnetism also causes electronegativity.
The longer answer is: what electron distribution develops in equilibrium around a set of positive nuclei (and hence, in a molecule) depends on the distribution of nuclei and their charges. It is quite intuitive that the electrons will feel more attracted to higher charged nuclei, just as in some circles, attractive women will feel more attracted to the guys with the most muscle mass, whereas the beardless beanpole will sip alone on his glass of orange juice at the party. But like in the mating case, the situation is a little more complicated with electronegativity, where the radius of orbitals also plays a role as to what nucleus attracts electrons the most.
Independent of the specific reasons for preferred attraction, a resulting charge distribution could be naively described by tabulating the charge density at regular picometer intervals in x, y, z direction, or it can be described by something called a multipole expansion. There is quite some math involved in multipole expansion, but the intuition behind it is basic. It describes the angular distribution of charge with respect to a certain reference point (for example the center of gravity of a molecule).
The zeroth order multipole (called "monopole") just describes a spherically symmetric charge distribution (same charge density in all directions). The first order multipole (called "dipole") describes a charge distribution where in one direction there is more positive charge and in the opposite direction there is more negative charge. The second order multipole (strangely called "quadrupole") describes a charge distribution which is shamrock-shaped, i.e. positive charge in two preferred opposite directions, and negative charge in the two opposite directions perpendicular to the former. This goes on, and on, and on ("octupoles", "hexadecupoles", etc.), up to infinite order. Usually, the intensity of the higher multipole moments is weaker by itself (which is a consequence of the multipole expansion being a convergent mathematical approximation method), but more importantly they get weaker much faster than 1/r (namely $1/r^2, 1/r^3\dots$).
Electronegativity simply deals with first order multipoles (dipoles) and tries to explain why it exists for a certain molecule, in basically the party metaphor I have chosen above. But there are infinitely many other types of charge asymmetry/multipoles, which do not have any specific names, but which are all just a special case of electromagnetic equilibrium states. Nevertheless, the electronegativity concept is very useful, simply because very often molecules are charge neutral (i.e. if we are not dealing with ions, the atoms/molecules have no monopole moment), so the next most important (strongest) charge "shape" is the dipole.
It's the electromagnetic force. An object being neutral does not mean no electric field- it just doesn't have a $1/r^2$ component to its electric field. A dipole moment will give it a $1/r^3$ component, and higher-order moments will give higher order components in $1/r$.
Every atom has a different distribution of electrons, and so has a different electric field. The different electronegativity of different atoms comes from these different electric fields.
When a reaction happens the Gibbs free energy had to be negative. $$\Delta G=-nFE=RT\ln(Q/K)=\mu\,\mathrm dN + V\,\mathrm dp+S\,\mathrm dT$$ So you can see that if the $E$ or the cell potential is large the reaction is spontaneous meaning that a electropositive reactant and an electronegative reactant will react spontaneously. You can also see that when you increase the temperature the energy levels of the orbitals changes and that most reactions (exothermic) can be reversed by increasing the temperature(the equilibrium constant $K$ is a function of $T$). The energy to take an electron from the highest occupied orbital to infinity in gas state is known as the ionization energy and the other is the electron affinity. So yes big bonds where the atoms are far apart are infact more reactive and typically where the molecule will react whereas bonds that are electrically polarized with the opposite charges close are less reactive(like ionic bonds). Also through the process of electrolysis you can once again inject electrons into the molecule and do nonspontaneous reactions just like by playing the temperature. The voltage applied has to at least be equal to the voltage of the spontaneous reaction calculated in the equation above(this is known as the decomposition potential).
