Show that electric field intensity is normal to equipotential surface.

Equipotential surfaces

The SI unit of electric field intensity is

The electric field lines pass through an equipotential surface _______. [Fill in the blank]

Explain— Electric field lines cut the equipotential surface normally.

Explain why, for any charge configuration the equipotential surface through a point is normal to the electric field at that point. Draw a sketch of equipotential surfaces due to a single charge (-q), depicting the electric field lines due to the charge.

Show that electric field intenstity on the surface of a charged conductor is vecE=sigma/ε_0 vecn where sigma is the surface density of charge and vecn is the outward pointing unit normal vector.

Prove that the electric field intensity at a point is equal to the negative gradient of electric potential at that point.

Electric field intensity is zero at a point. Is electric potential exist at the point?

Deduce the relation between electric field intensity and potential at a point in an electric field.