CBSE Class 12 Board Examination

Chapter 2: Electrostatic Potential and Capacitance

Summary

Electrostatic potential at a point is the work done per unit positive charge in bringing it from infinity to that point, \(V=\dfrac{1}{4\pi\varepsilon_0}\dfrac{q}{r}\) for a point charge. Potential is a scalar, making it easier to handle than the field, and the two are linked by \(\vec{E}=-\nabla V\); the field always points from high to low potential. Equipotential surfaces, on which \(V\) is constant, are everywhere perpendicular to field lines, and no work is done moving a charge along them. The electrostatic potential energy of a charge configuration is the total work done in assembling it. A conductor in equilibrium has zero field inside and a constant potential throughout, with charge residing on its surface. Dielectrics, when polarised, reduce the field inside by a factor of the dielectric constant. A capacitor stores charge and energy; its capacitance \(C=Q/V\) depends only on geometry and the dielectric. For a parallel-plate capacitor \(C=\dfrac{\varepsilon_0 A}{d}\), increased \(K\) times by a dielectric. Capacitors in series and parallel combine by reciprocal and direct sums respectively, and the energy stored is \(U=\tfrac{1}{2}CV^2\), residing in the field between the plates.

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