Electric Field and Potential

Electric Field and Potential

• The electric field obeys the superposition principle, and therefore, the electrostatic potential also follows the superposition principle.
• The potential due to a dipole is the sum of the potentials due to the charges q and –q.

Electric Potential and Work

• The potential energy of a charge q at a position r in an external field is given by qV(r), where V(r) is the external potential at the point r.
• The unit of energy, 1 electron volt (eV), is defined as 1.6 × 10^–19 J, which is the energy gained by an electron when accelerated by a potential difference of 1 volt.

Potential Energy of a System of Two Charges

• The potential energy of a system of two charges q1 and q2 in an external field is the sum of the work done in bringing each charge from infinity to its respective position.
• The work done in bringing q2 to its position includes the work done against the external field and the field due to q1.

Electric Field in a Conductor and a Dielectric

• In a conductor, the free charge carriers move and adjust themselves to cancel the external electric field, resulting in a net electrostatic field of zero within the conductor.
• In a dielectric, the external field induces a dipole moment by stretching or re-orienting the molecules, resulting in a net charge on the surface that opposes the external field.

Polar and Non-Polar Molecules

• Non-polar molecules have no permanent dipole moment due to their symmetrical structure, whereas polar molecules have a permanent dipole moment due to the separation of their centers of positive and negative charges.
• A dielectric with polar molecules develops a net dipole moment in an external electric field due to the alignment of individual dipoles with the field.

Polarisation

• The dipole moment per unit volume of a dielectric is called polarisation (P) and is denoted by the equation P = ε0 χe E, where χe is the electric susceptibility of the dielectric medium.

Capacitors

• A capacitor is a key element of ac circuits, used for storing charge and has important functions described in Chapter 7.
• The capacitance of a capacitor is limited by the amount of charge that can be stored without significant leaking.
• Common units of capacitance are its sub-multiples, such as 1 mF, 1 nF, and 1 pF.

The Parallel Plate Capacitor

• A parallel plate capacitor consists of two large plane parallel conducting plates separated by a small distance, with the intervening medium being vacuum or a dielectric.
• The effect of a dielectric medium between the plates increases the capacitance from its vacuum value.
• The dielectric constant of a substance can be viewed as a definition of the increase in capacitance when the dielectric is inserted fully between the plates of a capacitor.