Page:Electricity (1912) Kapp.djvu/96

92 By adopting a radius equal to unity we get for the surface the expression 4π, and for the total flux the expression Φ = 4π B. We know that the force on unit pole at unit distance is $Q × 1⁄1^{2}$ = Q. We also know that the force is B × 1 = B, from which it follows that B and Q are numerically equal, and hence we find as an expression for the total flux emanating from Q units of electric charge

Φ = 4π Q

The conception of lines of force is very useful in forming a mental picture of the properties of an electric field by mechanical analogy, but the analogy must not be taken in too literal a sense. We must not think of lines of force in the same way as we think of the stalks of corn in a field, namely, as physical lines each bound to a definite position. In adopting such a view we would be met at once by the difficulty that our unit charge, being placed midway between two lines of force, would not experience any force. This is contrary to experiment; we cannot find any place in a field of sensible magnitude where the force acting on unit charge is zero. To escape the difficulty some writers use the expression