Machines producing Electrification by Mechanical Work

The Measurement of Electric Potential.

206*.] In order to determine large differences of potential in absolute measure we may employ the attracted disk electrometer, and compare the attraction with the effect of a weight.

If at the same time we measure the difference of potential of the same conductors by means of the quadrant electrometer, we shall ascertain the absolute value of certain readings of the scale of the quadrant electrometer, and in this way we may deduce the value of the scale readings of the quadrant electrometer in terms of the potential of the suspended part, and the moment of torsion of the suspension apparatus. To ascertain the potential of a charged conductor of finite size we may con- nect the conductor with one electrode of the electrometer, while the other is connected to earth or to a body of constant potential. The electrometer reading will give the potential of the conductor after the division of its electricity between it and the part of the electrometer with which it is put in contact.

If K denote the capacity of the conductor, and K ′ that of this part of the elec- trometer, and if V , V ′ denote the potentials of these bodies before making contact, then their common potential after making contact will be V= KV + K ′ V ′ . K + K′ Hence the original potential of the conductor was V =V+ K′ (V − V ′ ). KPOTENTIAL AT ANY POINT IN THE AIR. 194 If the conductor is not large compared with the electrometer, K ′ will be comparable with K, and unless we can ascertain the values of K and K ′ the second term of the expression will have a doubtful value. But if we can make the potential of the electrode of the electrometer very nearly equal to that of the body before making contact, then the uncertainty of the values of K and K ′ will be of little consequence.

If we know the value of the potential of the body approximately, we may charge the electrode by means of a ‘replenisher’ or otherwise to this approx- imate potential, and the next experiment will give a closer approximation. In this way we may measure the potential of a conductor whose capacity is small compared with that of the electrometer.

To Measure the Potential at any Point in the Air.

207*.] First Method. Place a sphere, whose radius is small compared with the distance of electrified conductors, with its centre at the given point. Con- nect it by means of a fine wire with the earth, then insulate it, and carry it to an electrometer and ascertain the total charge on the sphere.

Then, if V be the potential at the given point, and a the radius of the sphere, the charge of the sphere will be −V a = Q, and if V ′ be the potential of the sphere as measured by an electrometer when placed in a room whose walls are connected with the earth, then Q = V ′ a, whence V + V ′ = 0, or the potential of the air at the point where the centre of the sphere was placed is equal but of opposite sign to the potential of the sphere after being connected to earth, then insulated, and brought into a room. This method has been employed by M. Delmann of Creuznach in measur- ing the potential at a certain height above the earth’s surface∗ . ∗ [Compare Art. 50.]POTENTIAL OF A CONDUCTOR. 195 Second Method. We have supposed the sphere placed at the given point and first connected to earth, and then insulated, and carried into a space sur- rounded with conducting matter at potential zero.

Now let us suppose a fine insulated wire carried from the electrode of the electrometer to the place where the potential is to be measured. Let the sphere be first discharged completely. This may be done by putting it into the inside of a vessel of the same metal which nearly surrounds it and making it touch the vessel. Now let the sphere thus discharged be carried to the end of the wire and made to touch it. Since the sphere is not electrified it will be at the potential of the air at the place. If the electrode wire is at the same potential it will not be affected by the contact, but if the electrode is at a different potential it will by contact with the sphere be made nearer to that of the air than it was before. By a succession of such operations, the sphere being alternately discharged and made to touch the electrode, the potential of the electrode of the electrometer will continually approach that of the air at the given point.

208*.] To measure the potential of a conductor without touching it, we may measure the potential of the air at any point in the neighbourhood of the conductor, and calculate that of the conductor from the result. If there be a hollow nearly surrounded by the conductor, then the potential at any point of the air in this hollow will be very nearly that of the conductor. In this way it has been ascertained by Sir W. Thomson that if two hol- low conductors, one of copper and the other of zinc, are in metallic contact, then the potential of the air in the hollow surrounded by zinc is positive with reference to that of the air in the hollow surrounded by copper.

Third Method. If by any means we can cause a succession of small bodies to detach themselves from the end of the electrode, the potential of the elec- trode will approximate to that of the surrounding air. This may be done by causing shot, filings, sand, or water to drop out of a funnel or pipe connected with the electrode. The point at which the potential is measured is that at which the stream ceases to be continuous and breaks into separate parts or drops.