Lecture 1.6 - Conductors in Electrostatic Equilibrium

ELEC2300

Conductors and Electrostatic Equilibrium

1. Electrostatic Equilibrium

   • The state where charges are not moving.
   • In a conductor, charges can move if there’s an electric force upon them.
   • When a conductor is placed in an electric field, charges will move around until they find their new positions and stop moving.

2. Charge Distribution in a Conductor

   • If a conductor is placed in an electric field, the charges (e.g., electrons in a metal) will respond to that field.
   • Negative charges would be pulled against the direction of the field, leading to more electrons on one side and a net positive charge on the other side.
   • This separation of positive and negative charges creates a new electric field inside the conductor.

3. Electric Field Inside a Conductor

   • The electric field inside a conductor in electrostatic equilibrium is zero.
   • If there was a residual field, it would cause a force on the charged particles, causing them to move and disrupting the equilibrium.

4. Electric Field at the Surface of a Conductor

   • The electric field at the surface of a conductor in electrostatic equilibrium is perpendicular to the surface.
   • The strength of the electric field at the surface is directly related to the surface charge density.

5. Potential of a Conducting Surface

   • The potential is the same everywhere inside a conductor and on its surface in electrostatic equilibrium.
   • Conducting surfaces are equipotential surfaces.

6. Applying Gauss’s Law

   • Gauss’s Law states that the electric flux through a closed surface is equal to the charge inside divided by a constant $\epsilon$.
   • The flux is the difficult part to calculate.
   • For a flat surface in a uniform field, the integral simplifies to the magnitude of the electric field times the area times the cosine of the angle between the normal to the surface and the electric field.
   • The flux is maximum when the surface is oriented face-on to the field and zero when the surface is side-on to the field.

7. Charge Inside a Conductor

   • Any excess charge in a conductor must be on the surface.
   • The surface charge density is the charge divided by the area.
   • The electric field strength on the surface of a conductor is directly related to the surface charge density and is given by $\frac{\sigma }{\epsilon }$, where $\sigma$ is the surface charge density and $\epsilon$ is the permittivity of free space.