Editing Content :: Admin Scraper

Chapter

Content type

Position

Value

Electrostatic Potential and Capacitance (ii) Equation (2.2) defines potential energy difference in terms of the physically meaningful quantity work. Clearly, potential energy so defined is undetermined to within an additive constant.What this means is that the actual value of potential energy is not physically significant; it is only the difference of potential energy that is significant. We can always add an arbitrary constant to potential energy at every point, since this will not change the potential energy difference: (UP+ α ) −(UR+ α ) = P −U R Put it differently, there is a freedom in choosing the point where potential energy is zero. A convenient choice is to have electrostatic potential energy zero at infinity. With this choice, if we take the point R at infinity, we get from Eq. (2.2) Count Alessandro Volta C (1745 – 1827) Italian O W ∞P = UP−U =∞U P (2.3) U physicist, professor at N Since the point P is arbitrary, Eq. (2.3) provides us with a Pavia. Volta established T definition of potential energy of a charge q at any point. that the animal electri- A Potential energy of charge q at a point (in the presence of field city observed by Luigi L due to any charge configuration) is the work done by the Galvani, 1737–1798, in E experiments with frog S external force (equal and opposite to the electric force) in muscle tissue placed in A bringing the charge q from infinity to that point. contact with dissimilar N metals, was not due to D 2.2 E LECTROSTATIC P OTENTIAL R any exceptional property O Consider any general static charge configuration. We define of animal tissues but V potential energy of a test charge q in terms of the work done was also generated O whenever any wet body L on the charge q. This work is obviously proportional to q, since was sandwiched between A the force at any point is qE, where E is the electric field at that dissimilar metals. This point due to the given charge configuration. It is, therefore, led him to develop the 1 convenient to divide the work by the amount of charge q, so first voltaic pile, or 7 5 that the resulting quantity is independent of q. In other words, battery, consisting of a – work done per unit test charge is characteristic of the electric large stack of moist disks 1 field associated with the charge configuration. This leads to of cardboard (electro- 8 the idea of electrostatic potential V due to a given charge lyte) sandwiched 7 between disks of metal ) configuration. From Eq. (2.1), we get: (electrodes). Work done by external force in bringing a unit positive charge from point R to P  U −U  = VP– VR = P R  (2.4)  q  where V Pnd V aRe the electrostatic potentials at P and R, respectively. Note, as before, that it is not the actual value of potential but the potential difference that is physically significant. If, as before, we choose the potential to be zero at infinity, Eq. (2.4) implies: Work done by an external force in bringing a unit positive charge from infinity to a point = electrostatic potential (V ) at that point. 47 Reprint 2026-27