418 PROBLEMS AND EXERCISES. 



vertical ordinates the amounts you have calculated for the 

 corresponding forces ; lastly, connecting by a curved line the 

 system of points thus found. 



5. Define electrostatic (or electric) "potential;" and calculate 

 (by the rule given in italics in Art. 238) the potential at a point 

 A, which is at one corner of a square of 8 centimetres' side, 

 when at the other three corners B, C, D, taken in order, 

 charges of + 16, +34, and +24 units are respectively placed. 



Am. 8, very nearly exactly. 



6. A small sphere is electrified with 24 units of + electricity. 

 Calculate the potential due to this charge at points I, 2, 3, 4, 5, 

 6, 8, and 10 centimetres' distance respectively. Then plot out 

 the "curve of potential" to scale, as described in Question 4. 



.7. What are equipotential surfaces? Why is the surface of 

 an insulated conductor an equipotential surface ? Is it always 

 so? 



8. A sphere whose radius is 14 centimetres is charged until 

 the surface density has a value of 10. What quantity of 

 electricity is required for this? Ans. 24,640 units (nearly). 



9. In the above question what will be the potential at the 

 surface of the sphere? (See last sentence of Art. 246.) 



Ans. 1760 (very nearly). 



10. In the case of question 8, what will be the electric force at 

 a point outside the sphere and indefinitely near to its surface ? 

 (Art. 251.) Ans. 1257 (very nearly). 



11. Suppose a sphere whose radius is 10 centimetres to be 

 charged with 6284 units of electricity, and that it is then caused 

 to share its charge with a non-electrified sphere whose radius is 

 15 centimetres, what will the respective charges and surface- 

 densities on the two spheres be when separated ? 



Ans. Small sphere, q 2513-6, 2 : 

 Large sphere, q = 377O'4> 9 = 1*33- 



12. A charge of + 8 units is collected at a point 20 centi- 

 metres distant from the centre of a metallic sphere whose radius 

 is 10 centimetres. It induces a negative electrification at the 

 nearest side of the sphere. Find a point inside the sphere such 

 that if 4 negative units were placed there they would exercise 



