PPT No. 6 * Electric Monopoles * Electric Dipoles * Field of a Dipole * Couple and Force on a Dipole • Energy of a Dipole * Force on Charged Conductor * Energy of Electrostatic Systems Electric Monopoles, Dipoles Electric Monopole An isolated single charge can be called an "electric monopole". Electric dipole Equal positive and negative charges placed close to each other constitute an electric dipole Electric Quadrupole Two oppositely directed dipoles close to each other are called an Electric Quadrupole Electric Dipoles An electric dipole is a separation of positive and negative charges. The simplest example of electric dipole is a pair of electric charges of equal magnitude but opposite sign, separated by some, usually small distance A permanent electric dipole is called an electret Electric Dipoles A physical dipole consists of two equal and opposite point charges: in the literal sense, two poles. Its field at large distances (distances large in comparison to the separation of the poles) Depends almost entirely on the dipole moment. Electric Field of a Dipole The electric field of an electric dipole is calculated by the vector sum of the point charge fields of the two charges: The electric field from a dipole can be found from the gradient of the potential where the Electrostatic potential at position r due to an electric dipole at the origin is given by: is a unit vector in the direction of r', p is the (vector) Dipole moment, and ε0 is the Permittivity of free space Moment of a Dipole Dipoles can be characterized by their Dipole moment. The electric dipole moment is a measure of the separation of positive and negative electrical charges in a system of charges. It is a vector quantity. The electric dipole moment is denoted by p Moment of a Dipole In the simple case the electric dipole moment p is defined for a pair of opposite point charges of magnitude q (one with charge + q and other with charge − q) as the strength (magnitude) of each charge q multiplied by the separation (distance) d between them: The direction is defined from the negative charge to the positive charge. Thus, the electric dipole moment vector p points from the negative charge to the positive charge. Couple and Force on a Dipole When a dipole is placed in an electric field E, equal but opposite forces act on each side of the dipole giving rise to a Torque τ: Torque τ = E q d sin θ Couple and Force on a Dipole Electric Dipole moment p is given by p = qd (in coulomb-meters), Torque τ = E q d sin θ τ =pXE Thus Torque can be expressed as a vector product and its direction is given by the right hand rule Electric Dipole and Torque Fig. Electric Dipole and Torque Energy of an Electric Dipole Fig Forces on dipole kept in an electric field Energy of an Electric Dipole The torque resulting from two equal and opposite charges q tends to align the electric dipole having Dipole moment p in the direction of applied field E, since it is the configuration having the lowest energy. To take it from this state of lowest energy, work has to be done against the electric field. It is stored as potential energy U given by Energy in the Electric Field The electric field stores energy. The energy density of the electric field is given by ε is the permittivity of the medium in which the field exists E is the electric field vector. Energy in the Electric Field The total energy stored in the electric field E in a given volume V is Where dV is the differential volume element ε is the permittivity of the medium

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