Electrostatic Potential and Capacitance
Class 12 Physics · Physics Part I · Chapter 2
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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.
Electric potential of charges and dipolesEquipotential surfacesPotential energy of charge systemsConductors and dielectricsCapacitance and parallel-plate capacitorCombinations and energy of capacitors
Key terms
Electrostatic potential
Work per unit positive charge to bring it from infinity to a point; scalar, unit volt.
Equipotential surface
A surface of constant potential; the field is perpendicular to it and no work is done along it.
Potential energy
Work done in assembling a charge configuration against electrostatic forces.
Capacitance
Ratio of stored charge to potential, \(C=Q/V\); SI unit farad.
Dielectric constant
Factor \(K\) by which a dielectric reduces the field and raises the capacitance.
Polarisation
Induced dipole moment per unit volume in a dielectric placed in a field.
Extra questions & answers
Try one from this chapter
The electric potential at a point due to a point charge +Q placed in vacuum is V. If the distance of the point from the charge is doubled, the new potential becomes