Question

give an experimental concept to store both bound and
free charge​

Answer 1

Answer:

5–1Electrostatics is Gauss’ law plus …

There are two laws of electrostatics: that the flux of the electric field from a volume is proportional to the charge inside—Gauss’ law, and that the circulation of the electric field is zero—E is a gradient. From these two laws, all the predictions of electrostatics follow. But to say these things mathematically is one thing; to use them easily, and with a certain amount of ingenuity, is another. In this chapter we will work through a number of calculations which can be made with Gauss’ law directly. We will prove theorems and describe some effects, particularly in conductors, that can be understood very easily from Gauss’ law. Gauss’ law by itself cannot give the solution of any problem because the other law must be obeyed too. So when we use Gauss’ law for the solution of particular problems, we will have to add something to it. We will have to presuppose, for instance, some idea of how the field looks—based, for example, on arguments of symmetry. Or we may have to introduce specifically the idea that the field is the gradient of a potential.

5–2Equilibrium in an electrostatic field

Consider first the following question: When can a point charge be in stable mechanical equilibrium in the electric field of other charges? As an example, imagine three negative charges at the corners of an equilateral triangle in a horizontal plane. Would a positive charge placed at the center of the triangle remain there? (It will be simpler if we ignore gravity for the moment, although including it would not change the results.) The force on the positive charge is zero, but is the equilibrium stable? Would the charge return to the equilibrium position if displaced slightly? The answer is no.

There are no points of stable equilibrium in any electrostatic field—except right on top of another charge. Using Gauss’ law, it is easy to see why. First, for a charge to be in equilibrium at any particular point P0, the field must be zero. Second, if the equilibrium is to be a stable one, we require that if we move the charge away from P0 in any direction, there should be a restoring force directed opposite to the displacement. The electric field at all nearby points must be pointing inward—toward the point P0. But that is in violation of Gauss’ law if there is no charge at P0, as we can easily see.