Page:Elementary Text-book of Physics (Anthony, 1897).djvu/302

288 force within a charged sphere is then, from § 57, consistent with the law of electrical force which has been given; and since the means of detecting electrical force, if there were any, within a charged conductor are very delicate, this fact affords a strong corroborative proof of the law.

The determination of the distribution of electricity on irregularly shaped conductors is in general beyond our power. If we consider, however, a conductor in the form of an elongated egg, it can be readily seen that, in order that there may be no electrical force within it, the surface density at the pointed end must be greater than that anywhere else on its surface. In general, the surface density at points on a conducting surface depends upon the curvature of the surface, being greater where the curvature is greater.

Thus, if the conductor be a long rod terminating in a point, the surface density at the pointed end is much greater than that anywhere else on the rod.

255. Unit Charge.—The law of electrical force enables us to define a unit charge, based upon the fundamental mechanical units. Let there be two equal and similar positive charges concentrated at points unit distance apart in air, such that the repulsion between them equals the unit of force. Then each of the charges is a unit charge, or a unit quantity of electricity. With this definition of unit charge, it may be said that the force between two charges is not merely proportional to, but equals, the product of the charges divided by the square of the distance between them. The factor $$k$$ in the expression for the force between two charges becomes unity, and the dimensions of $$\frac{QQ'}{r^2}$$ are those of a force. If the charges be equal, we have $$\left[ \frac{Q^2}{r^2} \right] = MLT^{-2}.$$ Hence $$[Q] = M^{\frac{1}{2}}L^{\frac{3}{2}}T^{-1}$$ are the dimensions of the charge. This equation gives the charge in absolute mechanical units, and by ineans of it all other electrical quantities may be expressed in absolute units. It is at the basis of the electrostatic system of electrical measurements.

The practical unit of charge or quantity is called the coulomb.