Applications of Equipotentials and Electrostatic Shielding

What is an Equipotential? In discussing equipotentials, we must admit that the earth must have the same potential with all over, because it is a conductor. In a conductor, there can be no differences of potential, because these would set up a potential gradient or electric field; electrons would then redistribute themselves throughout the conductor, under the influence of the field, until they had destroyed the field. This is true whether the conductor has a net charge, positive or negative, or whether it is uncharged; it is true whatever the actual potential of the conductor, relative to any other body.

Any surface of volume over which the potential is constant is called an equipotential. The volume or surface may be that of a material body, or simply a surface of volume in space. For example, as well shall see later, the space inside a hollow charged conductor is an equipotential volume. Equipotential surfaces can be drawn throughout any space in which there is an electric field, as we shall now explain.

Let us consider the field of an isolated point-charge Q. At a distance a from the charge, the potential is Q/4πƹ₀a; a sphere of radius a and centre at Q is therefore an equipotential surface, of potential Q/4πƹ₀a. In fact, all spheres centered on the charge are equipotential surfaces, whose potentials inversely proportional to their radii (Fig above). An equipotential surface has the property that, along any direction lying in the surface, there is no electric field; for there is no potential gradient. Equipotential surfaces are therefore always at right angles to lines of force, as shown in (Fig. above). This also shows numerical values proportional to their potentials. Since conductors are always equipotentials, if any conductors appear in an electric-field diagram the lines of force must always be drawn to meet them at right angles

When we set out to consider the electric field due to more charges than one, then we see the advantage of the idea of potential over the idea of field-strength. If we wish to find the field-strength E at the point P in (Fig above), due to the two charges Q₁ and Q₂, we have first to find the force exerted by each on a unit charge at P, and then to compound these forces by the parallelogram method. (See Fig. above). On the other hand, if we wish to find the potential due to each charge, potential at P, we merely calculate and add the potentials algebraically.

they have no direction: they do not point north, east, south, or west. Quantities which have direction, like forces are called ‘vectors’; they have to be added either by resolution into components, or by the parallelogram method. Either way is slow and clumsy, compared with the addition of scalars. For example, we can draw the equipotentials round a point-charge with compasses; if we draw two sets of them, as in Fig. above (i) or (ii), then by simple addition we can rapidly sketch the equipotentials around the two charges together.

And when we have plotted the equipotentials, they turn out to be more useful than lines of force. A line of force diagram appeals to the imagination, and helps us to see what would happen to a charge in the field. But it tells us little about the strength of the field – at the best, if it is more carefully drawn than most, we can only say that the field is strongest where the lines are closest. But equipotentials can be labeled with the values of potential they represent; and from their spacing we can find the actual value of the potential gradient, and hence the field-strength. The only difficulty in interpreting equipotential diagrams lies in visualizing the direction of the force on a charge; this is always at right angles to the curves.

What is Electrostatic Shielding?

Electrostatic Shielding: The fact that there is no electric field inside a close conductor, when it contains no charged bodies, was demonstrated by Faraday in a spectacular manner. He made for himself a large wire cage, supported it on insulators, and sat inside it with his electroscopes. He then has the cage charged by an induction machine until painful sparks could be drawn from its outside. Inside the cage Faraday sat in safety and comfort, and there was no deflection to be seen on even his most sensitive electroscope.

If we wish to protect any persons or instruments from intense electric fields(electrostatic shielding), therefore, we enclose them in hollow conductors; these are called ‘Faraday cages’, and are widely used in high – voltage measurements in industry.

We may also wish to prevent charges in one place from setting up an electric field beyond their immediate neighbourhood. To do this we surround the charges with a Faraday cage, and connect the cage to earth. The charges induced on the outside of the cage then runs to earth, and there is no external field. (When a cage is used to shield something inside it, it does not have to be earthed.)

Comparison Of Static And Current Phenomena

Broadly speaking, we may say that in electrostatic phenomena, we meet small quantities of charge, but great differences of potential. On the other hand in the phenomena of current electricity, the potential differences are great. Sparks and shock are common in electrostatics, because they require great potential differences; but they are rarely dangerous, because the total amount of energy available is usually small. On the hand, shocks and sparks in current electricity are rare, but, when the potential difference is great enough to cause them, they are likely to be dangerous.

These quantitative difference make problems of insulation much more difficult in electrostatic apparatus than in apparatus for use with currents. The high potentials met in electrostatics make leakage disappear rapidly. Any wood, for example, ranks as an insulator for current electricity, but a conductor in electrostatics. In electrostatic experiments we sometimes wish to connect a charged body to earth; all we have then to do is touch it.