There is a point charge +Q and a test charge +q
Q<--------------------r------------------------>------q------------------------------∞
To move q from infinity to a distance r from Q,
- Electric Force on q = (1/ 4piε.)(Qq/r^2)
- Applied Force = - (1/ 4piε.)(Qq/r^2)
When we move the test charge q for a small distance dr ,
Work Done = - (1/ 4piε.)(Qq/r^2)dr
So, the total work done, i.e. the electric potential Energy
= (∞ to r)∫ - (1/ 4piε.)(Qq/r^2)dr
= (1/ 4piε.)(Qq/r)
However,
Since dr and applied force are in same direction (take right hand side is +ve)
why the small distance is dr , but not -dr??
更新1:
To physics8801 : for increment of vector.. q is moving towards Q x-------------------r----------------><---dr--- x---------------------r+dr--------------------> The increment seems to be -dr....>.
更新2:
from r + dr to r