30, 31] Lines of Force 25 



the meaning of the electric intensity. There will be a definite intensity at 

 every point of the electric field, quite independently of the presence of small 

 charged bodies. 



A small charged body might, however, conveniently be used for exploring 

 the electric field and determining experimentally the direction of the electric 

 intensity at any point in the field. For if we suppose the body carrying a 

 charge e to be held by an insulating thread, both the body and thread being 

 so light that their weights may be neglected, then clearly all the forces 

 acting on the charged body may be reduced to two: 



(i) A force jRe in the direction of the electric intensity at the. point 

 occupied by e, 



(ii) the tension of the thread acting along the thread. 



For equilibrium these two forces must be equal and opposite. Hence the 

 direction of the intensity at the point occupied by the small charged body is 

 obtained at once by producing the direction of the string through the charged 

 body. And if we tie the other end of the thread to a delicate spring balance, 

 we can measure the tension of the string, and since this is numerically equal 

 to .Re, we should be able to determine R if e were known. We might in 

 this way determine the magnitude and direction of the electric intensity at 

 any point in the field. 



In a similar way, a float at the end of a fishing-line might be used to determine the 

 strength and direction of the current at any point on a lake. And, just as with the 

 electric intensity, we should only get the true direction of the current by supposing the 

 float to be of infinitesimal size. We could not imagine the direction of the current 

 obtained by anchoring a battleship in the lake, because the presence of the ship would 

 disturb the whole system of currents. 



II. Lines of Force. 



31. Let us start at any point in the electric field, and move a short 

 distance OP in the direction of the electric intensity at 0. Starting from P 

 let us move a short distance PQ in the direction of the intensity at P, 



Q 



FIG. 4. 



and so on. In this way we obtain a broken 'path OPQR..., formed of 

 a number of small rectilinear elements. Let us now pass to the limit- 

 ing case in which each of the elements OP, PQ, QR, ... is infinitely small. 

 The broken path becomes a continuous curve, and it has the property that 

 at every point on it the electric intensity is in the direction of the tangent 



