Can electric field exist tangential to an equipotential surface and how much work is done to move a charge on an equipotential surface?
No, the electric field cannot exist tangentially to an equipotential surface. Here's why:
Therefore, it's impossible for a tangential electric field to exist on an equipotential surface, as it would violate the core principles of both concepts.
As for the work done to move a charge on an equipotential surface, it's zero. Since all points have the same potential, there's no potential difference to overcome, and the electric field wouldn't exert any force in a tangential direction. The charge would simply move freely without experiencing any work done by the electric field.
Electric field cannot exist tangential to an equipotential surface because if the field lines are tangential, work will be done in moving a charge on the surface, which is against the theory of equipotential surface.In other words, if there were an electric field tangential to an equipotential surface, the electric potential would change along the surface, and therefore, it would not be an equipotential surface anymore. Therefore, the electric field lines always cross the equipotential surfaces perpendicularly. Now think if there were a electric field along the surface of Equipotential Surface then as per the equation mentioned above there must be some potential difference thereby the surface will no more be equipotential surface. That is why there is no field along the tangent to the surface of equipotential surface. No, an electric field cannot exist tangential to an equipotential surface. This is because an equipotential surface is defined as a surface in which every point has the same electric potential.The inside component will give rise to voltage drop but we know a perfect electric conductor has infinite conductivity, therefore we expect the voltage drop must be zero inside the conductor. To have this, the tangential component of E field has to be zero. It should be normal. With zero resistance there can't be a tangential electric field because for every tangential electric field there are surface charges that move resistance-free and accumulate at the ends of the conductor to cancel the field. To move a charge from one point to another, the work done is zero, which, in turn, means the tangential component of the electric field along the equipotential surface has to be zero. Since ΔV = 0, for equipotential surfaces, the work done is zero, W = 0. It is said that no work is done in moving a charge on an equipotential surface. Work done n ervipotential surface is zero as w = q (V A − V B) & V A = V B. In electrostatics, conductors behave as an equipotential surface. The angle between Electric field and an equipotential surface is always 900. This is because, when the potential becomes constant, the negative potential gradient also becomes zero, hence necessitating the need for Electric field to be always normal with surface.