THE ELECTRIC FIELD

Excerpts

• THE ELECTRIC FIELD

  Finally, when we contemplate the region occupied by the medium as being a part of space in which electric phenomena may be observed, we shall call this region the Electric Field.

• THE ELECTRIC FIELD

  Since, therefore, the force which acts on the ball depends partly on the charge of the ball and partly on its position and on the electrification of the system, it is convenient to regard this force as the product of two factors, one being the charge of the ball, and the other *the electromotive force at that point of the field which is occupied by the centre of the ball*.

• THE ELECTRIC FIELD

  This shews that there has been an actual transference of electricity from the one disk to the other, the direction of this transference being that of the electromotive force.

• THE ELECTRIC FIELD

  The force with which they tend to separate is proportional to the area of the disks, and it increases as the electromotive force increases, not, however, in the simple ratio of that force, but in the ratio of the square of the electromotive force.

• THE ELECTRIC FIELD

  The fact that the electromotive force at a point close to the surface of a conductor is perpendicular to the surface 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.

• THE ELECTRIC FIELD

  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.

• THE ELECTRIC FIELD

  A line of force in every part of its course passes from places of higher to places of lower potential.

• THE ELECTRIC FIELD

  In every case, wherever we find an electrified insulated body, we are sure to find at the boundaries of the insulating medium, wherever they may be, an equal amount of electrification of the opposite kind.

• THE ELECTRIC FIELD

  We call it an *insulating* medium when we regard it simply as retaining the charge on the surface of the electrified body. When we consider it as taking an important part in the manifestation of electric phenomena we shall use Faraday’s expression, and call it a *dielectric* medium. Finally, when we contemplate the region occupied by the medium as being a part of space in which electric phenomena may be observed, we shall call this region the Electric Field.

• THE ELECTRIC FIELD

  The measurement of small forces is always a difficult operation, and becomes almost impossible when the weight of the body acted on forms a disturbing force and has to be got rid of by the adjustment of counterpoises. The measurement of the charges of the disks, on the other hand, is much more simple.

• THE ELECTRIC FIELD

  The electrification of each disk is proportional to the electromotive force, and the mechanical force on the disk is proportional to its electrification and the electromotive force conjointly, that is, to the *square* of the electromotive force.

• THE ELECTRIC FIELD

  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, and becomes [-1.5ex]0pt4.2ex12(1 - n)e.

• THE ELECTRIC FIELD

  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.

• THE ELECTRIC FIELD

  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.

• THE ELECTRIC FIELD

  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 angles to it.

Equations

• THE ELECTRIC FIELD

  \tfrac{1}{4}(1 - n)e + (-ne) &= 0\text{,}

  The charge left on the first sphere after the second sphere has been discharged and the charge shared, plus the charge on the neutralised vessel, sums to zero, so the segment's removed charge is exactly balanced by the sphere's remaining charge.

• THE ELECTRIC FIELD

  n &= \tfrac{1}{5}\text{,}

  Solving the charge balance gives n = 1/5, so the segment covering one-fifth of the sphere's surface removes one-fifth of its total charge.

Problems

No exercises in this chapter.