Experiment 13: Coulomb’s Proof Plane

Experiment XIII. Coulomb’s Proof Plane

47.] If one of these disks be placed with one of its flat surfaces in contact with the surface of an electrified conductor and then removed, it will be found to be charged. If the disk is very thin, and if the electrified surface is so nearly flat that the whole surface of the disk lies very close to it, the charge of the disk will be nearly equal to that of the portion of the electrified surface which it covered. If the disk is thick, or does not lie very close to the electrified surface, its charge, when removed, will be somewhat greater.

This method of ascertaining the density of electrification of a surface was introduced by Coulomb, and the disk when used for this purpose is called Coulomb’s Proof Plane.

The charge of the disk is by Experiment XII proportional to the electromo- tive force at the electrified surface. Hence the electromotive force close to a conducting surface is proportional to the density of the electrification at that part of the surface.

Since the surface of the conductor is an equipotential surface, the elec- tromotive force is perpendicular to it. The fact that the electromotive force at a point close to the surface of a conductor is perpendicular to the sur- face and proportional to the density of the electrification at that point was first established experimentally by Coulomb, and it is generally referred to as Coulomb’s Law.

To prove that when the proof plane coincides with the surface of the con- ductor the charge of the proof plane when removed from the electrified con- ductor is equal to the charge on the part of the surface which it covers, we may make the following experiment.

A sphere whose radius is 5 units is placed on an insulating stand. A seg- ment of a thin spherical shell is fastened to an insulating handle. The radius of the spherical surface of the shell is 5, the diameter of the circular edge of the segment is 8, and the height of the segment is 2. When applied to the sphere it covers one-fifth part of its surface. A second sphere, whose radius is also 5, is placed on an insulating handle.

The first sphere is electrified, the segment is then placed in contact with it and removed. The second sphere is then made to touch the first sphere, removed and discharged, and then made to touch the first sphere again. The segment is then placed within a conducting vessel, which is discharged to earth, and then insulated and the segment removed. One of the spheres is then made to touch the outside of the vessel, and is found to be perfectly discharged.

Let e be the electrification of the first sphere, and let the charge removed by the segment be ne, then the charge remaining on the sphere is (1 − n)e. The charge of the first sphere is then divided with the second sphere, andELECTROMOTIVE FORCE AND POTENTIAL. 45 becomes 12 (1 − n)e. The second sphere is then discharged, and the charge is again divided, so that the charge on either sphere is 14 (1 − n)e. The charge on the insulated vessel is equal and opposite to that on the segment, and it is therefore −ne, and this is perfectly neutralized by the charge on one of the spheres; hence 1 (1 − n)e + (−ne) = 0, 4 from which we find n = 15 , or the electricity removed by the segment covering one-fifth of the surface of the sphere is one-fifth of the whole charge of the sphere.

Experiment XIV. Direction of Electromotive Force at a Point.

48.] A convenient way of determining the direction of the electromotive force is to suspend a small elongated conductor with its middle point at the given point of the field.

The two ends of the short conductor will become oppositely electrified, and will then be drawn in opposite directions by the electromotive force, so that the axis of the conductor will place itself in the direction of the force at that point. A short piece of fine cotton or linen thread, through the middle of which a fine silk fibre is passed, answers very well. The silk fibre, held by both ends, serves to carry the piece of thread into any desired position, and the thread then takes up the direction of the electric force at that place.

Experiment 15. Potential at any Point of the Field.

49.] Suspend two small uncharged metal balls in the field by silk threads, and then connect them by means of a fine metal wire fastened to the end of anPOTENTIAL DETERMINED BY ONE SPHERE.

ebonite rod. Remove the wire and the spheres separately, and then examine the charges of the spheres.

It will be found that the two spheres, if they have become electrified, have received equal and opposite charges. If the potentials at the points of the field occupied by the centres of the spheres are different, positive electrification will be transferred from the place of high to the place of low potential, and the sphere at the place of high potential will thus become charged negatively, and that at the place of low potential will become charged positively. These charges may be shewn to be proportional to the difference of potentials at the two places.

We have thus a method of determining points of the field at which the potential is the same. Place one of the spheres at a fixed point, and move the other about till, on connecting the spheres with a wire as before, no charge is found on either sphere. The potentials of the field at the points occupied by the centres of the spheres must now be the same. In this way a number of points may be found, the potential at each of which is equal to that at a given point.

All these points lie on a certain surface, which is called an equipotential surface. On one side of this surface the potential is higher, on the other it is lower, than at the surface itself.

We have seen that electricity has no tendency to flow from one part of such a surface to another. An electrified body, if constrained so as to be capable of moving only from one point of the surface to another, would be in equilibrium, and the force acting on such a body is therefore everywhere perpendicular to the equipotential surface.

Experiment XVI.

50.] We may use one sphere only, and after placing it with its centre at any given point of the field we may touch it for a moment with a wire con- nected to the earth. We may then remove the sphere and determine its charge. The charge of the sphere is proportional to the potential at the given point, a positive charge, however, corresponding to a negative potential.

RECIPROCAL METHOD

Equipotential Surfaces.

51.] In this way the potential at any number of points in the field may be ascertained, and equipotential surfaces may be supposed drawn corresponding to values of the potential represented by the numbers 1, 2, 3, &c. These surfaces will form a series, each, in general, lying within the pre- ceding surface and having the succeeding surface within it. No two distinct surfaces can intersect each other, though a particular equipotential surface may consist of two or more sheets, intersecting each other at certain lines or points.

The surface of any conductor in electric equilibrium is an equipotential surface. For if the potential at one point of the conductor is different from that at another point, electricity will flow from the place of higher potential to the place of lower potential till the potentials are rendered equal.