The size of the charge also affects the coulombic attraction. When there is a high number of protons, the positive charge increases. The increase in positive charge improves the strength of the nucleus and is able to pull the electrons which are even further away.

Does coulombic attraction increase across a period?

Effective nuclear charge increase more steadily going across a period (more protons but not more shells) than going down a group (more protons but also more shells).

Does force of attraction increase from left to right?

With a larger distance between the negatively-charged electron and the positively-charged nucleus, the force of attraction is relatively weaker. Therefore, electron affinity decreases. Moving from left to right across a period, atoms become smaller as the forces of attraction become stronger.