Electrostatic induction

Electrostatic induction, also known as "electrostatic influence" or simply "influence" in Europe and Latin America, is a redistribution of electric charge in an object that is caused by the influence of nearby charges. In the presence of a charged body, an insulated conductor develops a positive charge on one end and a negative charge on the other end. The nature of electrostatic induction was studied in the mid 1700s. Electrostatic generators, such as the Wimshurst machine, the Van de Graaff generator and the electrophorus, use this principle. Due to induction, the electrostatic potential (voltage) is constant at any point throughout a conductor. Electrostatic induction is also responsible for the attraction of light nonconductive objects, such as balloons, paper or styrofoam scraps, to static electric charges. Electrostatic induction laws apply in dynamic situations as far as the quasistatic approximation is valid.

Electrostatic induction, also known as "electrostatic influence" or simply "influence" in Europe and Latin America, is a redistribution of electric charge in an object that is caused by the influence of nearby charges. In the presence of a charged body, an insulated conductor develops a positive charge on one end and a negative charge on the other end. The nature of electrostatic induction was studied in the mid 1700s. Electrostatic generators, such as the Wimshurst machine, the Van de Graaff generator and the electrophorus, use this principle. Due to induction, the electrostatic potential (voltage) is constant at any point throughout a conductor. Electrostatic induction is also responsible for the attraction of light nonconductive objects, such as balloons, paper or styrofoam scraps, to static electric charges. Electrostatic induction laws apply in dynamic situations as far as the quasistatic approximation is valid.

The electrostatic field inside a conductive object is zero

(lines with arrows) of a nearby positive charge (+) causes the mobile charges in metal objects to separate. Negative charges (blue) are attracted and move to the surface of the object facing the external charge. Positive charges (red) are repelled and move to the surface facing away. These induced surface charges create an opposing electric field that exactly cancels the field of the external charge throughout the interior of the metal. Therefore, electrostatic induction ensures that the electric field everywhere inside a conductive object is zero.]] A remaining question is how large the induced charges are. The movement of charges is caused by the force exerted on them by the electric field of the external charged object, by Coulomb's law. As the charges in the metal object continue to separate, the resulting positive and negative regions create their own electric field, which opposes the field of the external charge. This process continues until very quickly (within a fraction of a second) an equilibrium is reached in which the induced charges are exactly the right size and shape to cancel the external electric field throughout the interior of the metal object. Then the remaining mobile charges (electrons) in the interior of the metal no longer feel a force and the net motion of the charges stops.

Induced charge resides on the surface

Since the mobile charges (electrons) in the interior of a metal object are free to move in any direction, there can never be a static concentration of charge inside the metal; if there was, it would disperse due to its mutual repulsion. Therefore, in induction, the mobile charges move through the metal under the influence of the external charge in such a way that they maintain local electrostatic neutrality; in any interior region the number of electrons per unit volume has the correct value so the negative charge of the electrons balances the positive charge of the nuclei. The electrons move until they reach the surface of the metal and collect there, where they are constrained from moving by the boundary. The surface is the only location where a net electric charge can exist. This establishes the principle that electrostatic charges on conductive objects reside on the surface of the object. External electric fields induce surface charges on metal objects that exactly cancel the field within.

The voltage throughout a conductive object is constant

The electrostatic potential or voltage between two points is defined as the energy (work) required to move a small positive charge through an electric field between the two points, divided by the size of the charge. If there is an electric field directed from point \mathbf{b} to point \mathbf{a} then it will exert a force on a charge moving from \mathbf{a} to \mathbf{b} . Work will have to be done on the charge by a force to make it move to \mathbf{b} against the opposing force of the electric field. Thus the electrostatic potential energy of the charge will increase. So the potential at point \mathbf{b} is higher than at point \mathbf{a} . The electric field \mathbf{E}(\mathbf{x}) at any point \mathbf{x} is the gradient (rate of change) of the electrostatic potential V(\mathbf{x}) : \nabla V = \mathbf{E}\, Since there can be no electric field inside a conductive object to exert force on charges (\mathbf{E} = 0)\, , within a conductive object the gradient of the potential is zero \nabla V = \mathbf{0}\, Another way of saying this is that in electrostatics, electrostatic induction ensures that the potential (voltage) throughout a conductive object is constant.

Text derived from https://en.wikipedia.org/w/index.php?oldid=1322038426 under CC BY-SA 4.0; modifications have been made.