Equipotential surface is defined as the surface where electric potential remains constant
so here voltage is constant
so on equipotential surface we know that
![\Delta V = 0](https://img.qammunity.org/2020/formulas/physics/high-school/zawbs3fmonf8rqkmsznt1eaz37akzemond.png)
so we know that work done is defined as
![W = q\Delta V](https://img.qammunity.org/2020/formulas/physics/high-school/hxu43iasr5sy7tghx658a8pg72ohkxp80h.png)
now we can say
![W = 0](https://img.qammunity.org/2020/formulas/physics/high-school/x8pbxhmtppyksdo48091cr4wwz3hmy6xva.png)
so work done on this surface must be zero