12 



ELECTRICAL ENGINEERING 



18. Potential and Potential Gradient in Special Cases. 



(a) Determine the potential and potential gradient in the field 

 surrounding an isolated sphere of radius R charged with Q units 

 of electricity. Fig. 10. 



FIG. 10. Potential and potential gradient near a charged sphere. 



The potential at a point P, distant r cm. from the centre of 

 the sphere is 



-? 



The potential gradient at P is 



de Q 



(14) 



and is equal to the electrostatic force at the point. 



Curve 1, Fig. 10, shows the variation of potential with distance 

 measured from the centre of the sphere. The equation of this 

 curve is 



Across the sphere the potential is constant and is equal to ^, 



but near the surface it falls off very rapidly. 



The potential gradient at any point is represented by the slope 

 of the tangent to the potential curve at that point; its values are 



