Physics Electrictrostatic potential

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Electrictrostatic potential

DIELECTRICS

Dielectrics are non-conducting substances. In contrast to conductors, they have no (or negligible number of ) charge carriers. when a conductor is placed in an external electric field. The free charge carriers move and charge distribution in the conductor adjusts itself in such a way that the electric field due to induced charges opposes the external field within the conductor. This happens until, in the static situation, the two fields cancel each other and the net electrostatic field in the conductor is zero. In a dielectric, this free movement of charges is not possible. It turns out that the external field induces dipole moment by stretching or re-orienting
molecules of the dielectric. The collective effect of all the molecular dipole moments is net charges on the surface of the dielectric which produce a field that opposes the external field. Unlike in a conductor, however, the opposing field so induced does not exactly cancel the external field. It only reduces it. The extent of the effect depends on the nature of the dielectric. To understand the
effect, we need to look at the charge distribution of a dielectric at the molecular level.

Dielectrics are non-conducting substances. In contrast to conductors, they have no (or negligible number of ) charge carriers. when a conductor is placed in an external electric field. The free charge carriers move and charge distribution in the conductor adjusts itself in such a way that the electric field due to induced charges opposes the external field within the conductor. This happens until, in the static situation, the two fields cancel each other and the net electrostatic field in the conductor is zero. In a dielectric, this free movement of charges is not possible. It turns out that the external field induces dipole moment by stretching or re-orienting
molecules of the dielectric. The collective effect of all the molecular dipole moments is net charges on the surface of the dielectric which produce a field that opposes the external field. Unlike in a conductor, however, the opposing field so induced does not exactly cancel the external field. It only reduces it. The extent of the effect depends on the nature of the dielectric. To understand the
effect, we need to look at the charge distribution of a dielectric at the molecular level.

Polarization

In an external electric field, the positive and negative charges of a nonpolar molecule are displaced in opposite
directions. The displacement stops when the external force on the constituent charges of the molecule is balanced by
the restoring force (due to internal fields in the molecule). The non-polar molecule thus develops an induced dipole moment.
The dielectric is said to be polarised by the external field. We consider only the simple situation when the induced dipole moment is in the direction of the field and is proportional to the field strength. (Substances for which this assumption is true are called linear isotropic dielectrics.) The induced dipole moments of different molecules add up giving a net dipole moment of the dielectric in the presence of the external field.

Thus in either case, whether polar or non-polar, a dielectric develops a net dipole moment in the presence of an external field. The dipole moment per unit volume is called polarisation and is denoted by P. For linear isotropic dielectrics,

`P = χ_e E`

where `χ_e` is a constant characteristic of the dielectric and is known as the electric susceptibility of the dielectric medium.
It is possible to relate `χ_e` to the molecular properties of the substance, but we shall not pursue that here.

Thus the polarised dielectric is equivalent to two charged surfaces with induced surface charge densities, say `σ_p` and `-σ_p`. Clearly, the field produced by these surface charges opposes the external field. The total field in the dielectric is, thereby, reduced from the case when no dielectric is present. We should note that the surface charge density `-σ_p` arises from bound (not free charges) in the dielectric.

In an external electric field, the positive and negative charges of a nonpolar molecule are displaced in opposite
directions. The displacement stops when the external force on the constituent charges of the molecule is balanced by
the restoring force (due to internal fields in the molecule). The non-polar molecule thus develops an induced dipole moment.
The dielectric is said to be polarised by the external field. We consider only the simple situation when the induced dipole moment is in the direction of the field and is proportional to the field strength. (Substances for which this assumption is true are called linear isotropic dielectrics.) The induced dipole moments of different molecules add up giving a net dipole moment of the dielectric in the presence of the external field.

Thus in either case, whether polar or non-polar, a dielectric develops a net dipole moment in the presence of an external field. The dipole moment per unit volume is called polarisation and is denoted by P. For linear isotropic dielectrics,

`P = χ_e E`

where `χ_e` is a constant characteristic of the dielectric and is known as the electric susceptibility of the dielectric medium.
It is possible to relate `χ_e` to the molecular properties of the substance, but we shall not pursue that here.

Thus the polarised dielectric is equivalent to two charged surfaces with induced surface charge densities, say `σ_p` and `-σ_p`. Clearly, the field produced by these surface charges opposes the external field. The total field in the dielectric is, thereby, reduced from the case when no dielectric is present. We should note that the surface charge density `-σ_p` arises from bound (not free charges) in the dielectric.

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