10 Conductors and Capacitors

Describe the charge distribution within a conductor.

• An ideal conductor is a material in which electrons are able to move freely.
• When a conductor is in electrostatic equilibrium, mutual repulsion of excess charge carriers results in those charge carriers residing entirely on the surface of the conductor.
  • i. In a conductor with a negative net charge, excess electrons reside on the surface of the conductor.
  • ii. In a conductor with a positive net charge, the surface becomes deficient in electrons, and can be modeled as if positive charge carriers reside on the surface of the conductor.
• Excess charges will move to the surface of a conductor to create a state of electrostatic equilibrium within the conductor.
  • i. The time interval over which charges reach electrostatic equilibrium within a conductor is so short as to be negligible.
  • ii. When a conductor reaches electrostatic equilibrium, all points on the surface of the conductor have the same electric potential, and the conductor becomes an equipotential surface.
  • iii. The charge density on the surface of a conductor will be greater where there are points or edges compared to planar areas.
• All excess charges reside on the surface of a conductor, which means there is no net charge in the interior of the conductor, and the electric field is zero within the conductor.
• The electric field is perpendicular to the outer surface of a conductor.
• A conductor can be polarized in the presence of an external electric field. This is a consequence of the conductor remaining an equipotential surface.
• Electrostatic shielding is the process of surrounding an area with a closed, conducting shell to create a region inside the conductor that is free from external electric fields.

Describe the movement of charge and the resulting interactions when conductors physically contact each other.

• When conductors are in electrical contact, charges will be redistributed such that the surfaces of each conductor are at the same electric potential.
• Ground is an idealized reference point that has zero electric potential and can absorb or provide an infinite amount of charge without changing its electric potential.
• Charge can be induced on a conductor by grounding the conductor in the presence of an external electric field. TOPIC 10.3 Capacitors

Describe the physical properties of a parallel-plate capacitor.

• A parallel-plate capacitor consists of two separated parallel conducting surfaces that can hold equal amounts of charge with opposite signs.
• Capacitance relates the magnitude of the charge stored on each plate to the electric potential difference created by the separation of those charges. Relevant equation:
  • i. The capacitance of a capacitor depends only on the physical properties of the capacitor, such as the capacitor’s shape and the material used to separate the plates.
  • ii. The capacitance of a parallel-plate capacitor is proportional to the area of one of its plates and inversely proportional to the distance between its plates. The constant of proportionality is the product of the dielectric constant, , of the material between the plates and the electric permittivity of free space, Relevant equation:
• The electric field between two charged parallel plates with uniformly distributed electric charge, such as in a parallel-plate capacitor, is constant in both magnitude and direction, except near the edges of the plates.
  • i. The magnitude of the electric field between two charged parallel plates, where the plate separation is much smaller than the dimensions of the plates, can be determined by applying Gauss’s law and the principle of superposition. Derived equation:
  • ii. The electric field is proportional to the surface charge density on either plate of the capacitor.
  • iii. A charged particle between two oppositely charged parallel plates undergoes constant acceleration, and therefore its motion shares characteristics with the projectile motion of an object with mass in the gravitational field near Earth’s surface.
• The electric potential energy stored in a capacitor is equal to the work done by an external force to separate that amount of charge on the capacitor.
• The electric potential energy stored in a capacitor is described by the equation . BOUNDARY STATEMENT While other shapes are also able to separate charges, AP Physics C: Electricity & Magnetism only expects the quantitative analysis and description of parallel-plate capacitors, concentric spherical capacitors, and coaxial cylindrical capacitors.

Describe how a dielectric inserted between the plates of a capacitor changes the properties of the capacitor.

• In a dielectric material, electric charges are not as free to move as they are in a conductor. Instead, the material becomes polarized in the presence of an external electric field.
• The dielectric constant of a material relates the electric permittivity of that material to the permittivity of free space. Relevant equation:
• The electric field created by a polarized dielectric is opposite in direction to the external field.
• The electric field between the plates of an isolated parallel-plate capacitor decreases when a dielectric is placed between the plates. Derived equation:
• The insertion of a dielectric into a capacitor may change the capacitance of the capacitor. Derived equation: TOPIC 11.1 Electric Current