Electric Fields in Conductors

In electrostatics, an ideal conductor contains free charges that can move. This creates three high-yield results in H3:

1. the conductor is an equipotential volume,
2. the electric field inside the conductor is zero, and
3. the electric field at the surface is normal to the surface. Any excess charge resides on a surface; with an empty enclosed cavity, it resides on the outer surface.

1. Definitions (Must Know)

• Ideal conductor: a material with mobile charges that can move freely in response to an electric field.
• Electrostatic equilibrium: charges are at rest (no net drift).
• Equipotential volume: electric potential V is the same everywhere inside the conductor and on its surface.
• Electric field inside an ideal conductor (electrostatic): vector E = vector 0.
• Field at conductor surface: the electric field has no tangential component, so it is perpendicular (normal) to the surface.
• Symbols used in this lesson: vector E electric field (N C⁻¹ or V m⁻¹), Eₜ tangential field component at a surface (V m⁻¹), V electric potential (V), q charge (C), vector F force (N).

2. Key Ideas (What Earns Marks)

• If vector E ≠ vector 0 inside a conductor, free charges experience a force and move, so it cannot be electrostatic equilibrium.
• In equilibrium, the surface of a conductor is an equipotential; otherwise charges would move along the surface.
• The “vector E is normal to the surface” statement is really: tangential component Eₜ = 0 at the surface.

Quick comparison:

3. Detailed Explanations

A. Why vector E = vector 0 inside a conductor (electrostatic equilibrium)

If an electric field existed inside the conductor, a free charge q would experience: vector F = q vector E So charges would accelerate and redistribute until the internal field cancels to zero.

Therefore, in electrostatic equilibrium: vector E_inside = vector 0

B. Why a conductor is an equipotential volume

Electric field relates to potential gradient: vector E = - vector ∇V If vector E = vector 0 everywhere inside the conductor, then the potential cannot change with position inside it. So V is constant throughout the conductor (an equipotential volume).

C. Why vector E is perpendicular to the surface

Suppose the electric field at the surface had a non-zero tangential component Eₜ along the surface. A surface charge would then feel a tangential force and move along the surface, contradicting electrostatic equilibrium.

So at the surface: Eₜ = 0 and the field is purely normal to the surface.

4. Common Mistakes

• Forgetting the condition “electrostatic equilibrium” (if charges are moving or fields vary with time, the conclusions can change).
• Saying “the field is zero at the surface” (false in general; it is the tangential component that is zero).
• Mixing “equipotential surface” with “no electric field”: equipotential only implies no field component along the surface.

5. Exam Tips

• Use mark-scheme-safe phrasing:
  • “In electrostatic equilibrium, vector E = 0 inside an ideal conductor.”
  • “Charge resides on the surface; the field at the surface is normal to the surface.”
• If asked “why?”, always state the driver: “otherwise charges would move”.
• Link idea: equipotential ⇒ no tangential component of vector E.

6. Worked Examples

7. Mind Stretchers

8. Optional/Enrichment

A. Quantitative “just outside the surface” result (Gauss law)

Using Gauss’s law with a small “pillbox” surface gives a quantitative relation for the field just outside a conductor in vacuum in terms of surface charge density. This derivation is not needed for this lesson; it fits better under Gauss’s law.

For a deeper (university) treatment:

• UY1: Gauss’s Law For Conductors

For the A Level potential/field link (equipotentials and tangential components):

• Equipotential Line

Next step

Continue to Gauss’s Law to turn these conductor results into a closed-surface flux method.