the width of a large-scale confidence interval for p if the confidence level and p-hat (sample proportion) are constant and n (sample size) increases?...

What happens to the width of a large-scale confidence interval for p if the confidence level and p-hat (sample proportion) are constant and n (sample size) increases?

1) The interval width increases.

2) The interval width decreases.

3) The interval width stays the same.

4) You cannot tell without more information.

Please carefully explain the reasoning for the answer in clear English sentences. I don't want just the answer. I want to make sure that I understand the concepts leading to the right answer.