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www.GOALias.blogspot.comPhysicswill immediately flow onto the matter, eventhough the charge Q may be quite large. Thenatural tendency is for positive charge tomove from higher to lower potential. Thus,provided we are somehow able to introducethe small charged sphere into the larger one,we can in this way keep piling up larger andlarger amount of charge on the latter. Thepotential (Eq. 2.78) at the outer sphere wouldalso keep rising, at least until we reach thebreakdown field of air.This is the principle of the van de Graaffgenerator. It is a machine capable of buildingup potential difference of a few million volts,and fields close to the breakdown field of airwhich is about 3 × 10 6 V/m. A schematicdiagram of the van de Graaff generator is givenin Fig. 2.33. A large spherical conductingFIGURE 2.33 Principle of construction shell (of few metres radius) is supported at aof Van de Graaff generator.height several meters above the ground onan insulating column. A long narrow endlessbelt insulating material, like rubber or silk, is wound around two pulleys –one at ground level, one at the centre of the shell. This belt is keptcontinuously moving by a motor driving the lower pulley. It continuouslycarries positive charge, sprayed on to it by a brush at ground level, to thetop. There it transfers its positive charge to another conducting brushconnected to the large shell. Thus positive charge is transferred to theshell, where it spreads out uniformly on the outer surface. In this way,voltage differences of as much as 6 or 8 million volts (with respect toground) can be built up.SUMMARY841. Electrostatic force is a conservative force. Work done by an externalforce (equal and opposite to the electrostatic force) in bringing a chargeq from a point R to a point P is V P– V R, which is the difference inpotential energy of charge q between the final and initial points.2. Potential at a point is the work done per unit charge (by an externalagency) in bringing a charge from infinity to that point. Potential at apoint is arbitrary to within an additive constant, since it is the potentialdifference between two points which is physically significant. If potentialat infinity is chosen to be zero; potential at a point with position vectorr due to a point charge Q placed at the origin is given is given by1 QV ( r)=4 πεor3. The electrostatic potential at a point with position vector r due to apoint dipole of dipole moment p placed at the origin is1 ˆV ( ) = pr gr π 2ε r4 o