71, 72] Examples 63 



REFERENCES. 



On the general theory of Electrostatic Forces and Potential : 



MAXWELL. Electricity and Magnetism. Oxford (Clarendon Press). Chap. n. 

 THOMSON AND TAIT. Natural Philosophy. Cambridge (Univ. Press). Chap. vi. 



On Cavendish's experiment on the Law of Force : 



CAVENDISH. Electrical Researches. Experimental determination of the Law of 

 Electric Force ( 217235), and Note 19. 



On Examples of Fields of Force : 



MAXWELL. Electricity and Magnetism, Chaps, vi, vn. 



> 



T ^ 



EXAMPLES. 



1. Two particles each of mass m and charged with e units of electricity of the same 

 sign are suspended by strings each of length a from the same point; prove that the 

 inclination B of each string to the vertical is given by the equation 



sin 3 0=e 2 cos#. 



2. Charges + 4e, e are placed at the points A, B, and C is the point of equilibrium. 

 Prove that the line of force which passes through C meets AB at an angle of 60 at A and 

 at right angles at C. 



3. Find the angle at A (question 2) between AB and the line of force which leaves B 

 at right angles to AB. 



4. Two positive charges e\ and e 2 are placed at the points A and B respectively. 

 Shew that the tangent at infinity to the line of force which starts from ei making an angle 

 a with BA produced, makes an angle 



with BA, and passes through the point C in AB such that 



AC : CB=e 2 : e^. 



5. Point charges +e, e are placed at the points A, B. The line of force which leaves 

 A making an angle a with AB meets the plane which bisects AB at right angles, in P. 

 Shew that 



.a ,- . PAB 



6. If any closed surface be drawn not enclosing a charged body or any part of one, 

 shew that at every point of a certain closed line on the surface it intersects the equi- 

 potential surface through the point at right angles. 



7. The potential is given at four points near each other and not all in one plane. 

 Obtain an approximate construction for the direction of the field in their neighbourhood. 



