Question

Why do the equipotential surfaces get closer to each other near the point charges

Answer 1

We know The relation between electric field and potential due to charge is given by

E = dV/R

Thus if dV is constant then

R  is inversely proportional to E

Thus all equipotential surfaces are closer at higher value of E.

For Any charge E is higher near charge thus equipotential surfaces are closely located nearer to the charge. They tend to spread out as we move away from charge.