Electrostatic Potential and Capacitance

Electric field is perpendicular to equipotential surfaces, No work is done in moving a charge along an equipotential surface, All points on an equipotential surface have the same potential

Electric field is always perpendicular to equipotential surfaces. Since all points have the same potential, no work is done in moving charges along the surface. Equipotential surfaces cannot intersect as this would mean a point has two different potentials. Electric field lines are perpendicular, not parallel, to equipotential surfaces.

U = kq₁q₂/r

The potential energy of two point charges is U = kq₁q₂/r, where k = 1/(4πε₀). This represents the work done in bringing the charges from infinite separation to distance r. The energy is positive for like charges and negative for unlike charges.

Electric field inside is zero, Electric potential is constant throughout, Charges reside only on the surface, Electric field at surface is perpendicular to surface

In electrostatic equilibrium, conductors have zero electric field inside, constant potential throughout, charges only on the surface, and electric field perpendicular (not parallel) to the surface at every point.

Only the initial and final positions

Electrostatic force is conservative, so work done depends only on the initial and final positions, not on the path taken. This is why we can define electric potential as a state function. The speed and time of movement don't affect the work done.