Electrostatic Potential and Capacitance

Electric potential at point in an electric field is defined as the work done in moving a unit positive charge from infinity to that point. Electric potential is the scalar counterpart of electric field. Electrostatic potential due to a point charge is the ratio of charge to position vector from the origin. Potential due to a dipole depends not just on r but also on the angle between the position vectors. There are bodies which have same value of potential at each point all over their surface. Such surfaces are called equipotential surfaces. Potential varies with the distance from charge creating the field. Electric field is in a direction in which potential decreases fastest. The magnitude of electric field at a point is change in magnitude of potential per unit displacement normal to the equipotential surface at that point. Due to electric potential, the charges possess a potential energy. The potential energy of the system of two charges is the total work done in assembling the configuration. Conductors are the substances having mobile charge carriers. Dielectrics are insulators which do not conduct electricity. However, when an external field applied, included charges are produced on them. These materials do not have mobile charge carriers and hence the induced electric field in them doesn’t cancel out the external field. A capacitor consists of two conductors of arbitrary shape. These two conductors are said to be the plates of the capacitor. Depending on the shape of the plates, capacitors can be classified as parallel plate capacitor, spherical capacitor or cylindrical capacitor. Capacitance of a capacitor is the ratio of charge that can be given to it to the potential difference. It depends on the geometrical shape of the plates and the medium between the plates. The medium between plates is generally dielectric. A parallel plate capacitor is formed when two large plane conducting plates are separated by a small distance. A parallel plate is an arrangement which can be charged to large extent in a small area. A dielectric medium of dielectric constant K when placed between the plates of a parallel plate capacitor, the capacitance of the capacitor increases K times. Just like resistors, capacitors can be connected in series and parallel. In series combination, capacitors are connected end to end. The equivalent capacitance in this case is always less than the individual capacitance. In parallel combination, capacitors are connected such that their plates are connected to a common point. The equivalent capacitance in this case is always greater than the individual capacitance. During the process of charging a capacitor, a work has to be done in transferring the charge from the plate at lower potential to plate at higher potential. This work gets stored as the potential energy of the capacitor.

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