What is the angle between the electric field and tangent to the equipotential surface?

CONCEPT:

• Equipotential surface: Any surface that has the same electric potential at every point on it is called an equipotential surface.
• Relationship between the electric field (E), electric potential (V) and distance (r) is given by -

• \(dE = - \frac{{dV}}{{dr}}\)
• The electric field is a derivative of potential difference.
• The negative sign shows that the direction of E is opposite to the direction of dv i.e., dv decrease along the direction of E.

EXPLANATION:

• The electric field is always normal to the equipotential surface at every point.
• If the field were not normal to the equipotential surface, it would have a non-zero component along the surface.
• So to move a test charge against this component, work would have to be done.
• But there is no potential difference between any two points on an equipotential surface and consequently, no work is required to move a test charge on the surface.
• Hence the electric field must be normal to the equipotential surface at every point. Therefore option 4 is correct.