Experiment 17: Coulomb’s Proof Plane

Experiment 17.

52.] To make an experimental determination of the equipotential surfaces belonging to an electrified system we may use a small exploring sphere per- manently connected by a fine wire with one electrode of the electroscope, the other electrode being connected with the earth. Place the centre of the sphere at a given point, and connect the electrodes together for an instant.

The indication of the electroscope will thus be reduced to zero. If the sphere is now moved in such a manner that the indication of the electrometer remains zero during the motion, the path of the centre of the exploring sphere will lie on an equipotential surface. For if it moves to a place of higher potential, electricity will flow from the sphere to the electroscope, and if it moves to a place of lower potential, electricity will flow from the electroscope to the sphere.

If the bodies belonging to the electrified system are not perfectly insulated, their potentials and the potentials of the points of the field will tend to ap- proach zero. The path in which the centre of the exploring sphere moves is such that its potential at any point has a given value at the time when the centre of the sphere passes it. The different points of the path are not therefore on a surface which has the same potential at any one instant, for the potential is diminishing everywhere, and the path must therefore pass from surfaces of lower to surfaces of higher potential so as to make up for this loss.

Experiment XVIII

53.] The following method, founded on Theorem V, Art. 37, is therefore in many cases more conve- nient, as it is much eas- ier to secure good insulation for the exploring sphere on an insulating handle than for a large electrified conductor of irregular form. Let it be required to determine the equipotential surfaces due to the electrification of the con- ductor C placed on an in- sulating stand. Connect the conductor with one electrode of the electroscope, the other being connected with the earth. Electrify the explor- ing sphere, and, carrying it by the insulating handle, Fig. 16. bring its centre to a given point. Connect the electrodes for an instant, and then move the sphere in such a path that the indication of the electroscope remains zero. This path will lie on an equipotential surface.

For by Theorem V, the part of the potential of the conductor C due to the presence of the charged exploring sphere with its centre at a given point is equal to the potential at the given point due to a charge on the conductor C equal to that of the exploring sphere. By this method the potential of the conductor remains zero, or very nearlyLINES OF ELECTRIC FORCE. 49 zero, during the whole time of the experiment, so that there is very little tendency to change of the charge of this body. The exploring sphere, on the other hand, is at a high potential, but as it is not connected by a wire with any other body, its insulation may be made very good.

Lines of Electric Force.

54.] If the direction of the electric force at various points of the field be determined, and if a line be drawn so that its direction at every point of its course coincides with the direction of the electric force at that point, such a line is called a Line of Force. By drawing a number of such lines, the direction of the force at different parts of the field may be indicated. The lines of force and equipotential surfaces may be drawn, not in the electric field itself, where the mechanical operation of drawing them might produce disturbance, but in a model or plan of the electric field. Drawings of this kind are given in Plates I to VI at the end of the volume. Since the electric force is everywhere perpendicular to the equipotential surfaces, the lines of force cut these surfaces everywhere at right angles. The lines of force which meet the surface of a conductor are therefore at right an- gles to it. When they issue from the surface the electrification is positive, and when they enter the surface of the conductor the electrification is negative. A line of force in every part of its course passes from places of higher to places of lower potential.

The extremities of the same line of force are called corresponding points. The beginning of the line is a point on a positively electrified surface, and the end of the line is a corresponding point on a negatively electrified surface. The potential of the first of these surfaces must be higher than that of the second.