Why are electric field lines perpendicular to conducting surfaces?

Electric field lines are perpendicular to conducting surfaces because conductors redistribute their charges to cancel the field within themselves.

In more detail, when an external electric field is applied to a conductor, the free electrons within the conductor start to move. These electrons move in a direction opposite to the applied field until they reach the surface of the conductor. This movement of electrons creates an induced electric field inside the conductor. The induced field is in the opposite direction to the applied field, and the electrons continue to move until these two fields cancel each other out. This results in a net electric field of zero inside the conductor.

The charges that have moved to the surface of the conductor create a surface charge distribution. This distribution is such that the electric field just outside the conductor is perpendicular to the surface at every point. This is because the electric field lines must start or end on charges, and the charges are now on the surface of the conductor. Therefore, the electric field lines are perpendicular to the surface of the conductor.

To further understand the nature of electric fields around conductors, reviewing the basics of electric fields can provide foundational knowledge. Similarly, the concept of electric potential energy is closely related, explaining how potential energy varies in an electric field, which complements the understanding of electric fields being perpendicular to surfaces.

Additionally, exploring equipotential surfaces can enhance understanding of how electric potential remains constant on the surface of conductors, further illustrating why electric field lines are perpendicular to conducting surfaces. Understanding the material properties such as resistivity and conductivity also plays a significant role in comprehending the behaviour of conductors in electric fields.

This phenomenon is a direct consequence of two fundamental properties of conductors in electrostatic equilibrium. Firstly, the electric field inside a conductor in electrostatic equilibrium is zero. Secondly, the electric field just outside a conductor in electrostatic equilibrium is perpendicular to the conductor's surface. These properties ensure that the electric field lines are always perpendicular to the surface of a conductor.

IB Physics Tutor Summary: Electric field lines are perpendicular to conducting surfaces because conductors adjust their charge distribution to nullify the internal electric field. When an external field is applied, electrons move, creating an opposite internal field that cancels out the external one. This results in zero net field inside and perpendicular electric field lines at the surface.