Why are electric field lines perpendicular at a point on an equipotential surface of a conductor .
the work done on a test charge q moving in an electric field is the force q*E times the distance moved IN THE DIRECTION of the force. The only direction that has NO component of force in the direction of motion is in the direction perpendicular to the force. The force is in the direction of E. Therefore the direction where no work is done so no change in potential energy is perpendicular to E. That is the equipotential.
The perpendicularity of electric field lines at a point on an equipotential surface of a conductor can be explained based on the properties of the electric field and the behavior of conductors.
In order to understand this phenomenon, we need to consider the following key concepts:
1. Electric field lines: Electric field lines represent the direction and magnitude of the electric field at different points in space. They point in the direction of the force experienced by a positive test charge placed at that point.
2. Equipotential surfaces: These surfaces are imaginary surfaces in which all points have the same electrical potential. In the case of a conductor, the equipotential surfaces correspond to the surface of the conductor itself.
3. Conductors: In the case of conductors, the charges are free to move within the material. When an external electric field is applied, the charges redistribute themselves on the surface of the conductor, establishing an equilibrium state.
Now, let's explain why electric field lines are perpendicular to the equipotential surface at a point on a conductor:
- Inside a conductor: Within a conductor, the charges are in an equilibrium state and the electric field is zero. This means that there are no electric field lines inside the conductor and the electric potential is constant throughout.
- At the surface of a conductor: The charges on the surface of the conductor redistribute themselves in such a way that the electric field inside the conductor is zero. This is achieved by the charges rearranging themselves until they reach an equilibrium state, and the electric field becomes perpendicular to the surface. The reason for this behavior is that any tangential component of the electric field would cause the charges to move, which is forbidden in the equilibrium state of a conductor.
- Equipotential surface: Since the electric field is perpendicular to the surface of a conductor, the equipotential surfaces at the surface of the conductor are also perpendicular to the electric field lines. This is because the equipotential surfaces represent regions of equal potential, and since there is no potential difference along the surface of the conductor, the electric field lines must be perpendicular to these surfaces.
In summary, the reason why electric field lines are perpendicular at a point on an equipotential surface of a conductor is due to the redistribution of charges on the conductor's surface, which leads to an equilibrium state with a zero electric field inside the conductor and perpendicular electric field lines at the surface.