Why my external work equals the negative of the work done by electric force if i move positive test charge from infinity to a certain point in the electric field of positive charge

  • $\begingroup$ Is this a homework question? $\endgroup$ – probably_someone Sep 10 '18 at 22:33
  • $\begingroup$ No i studied the lesson And have some questions $\endgroup$ – Ahmad Eldesokey Sep 10 '18 at 22:34

Bringing a test change from infinity to a specified location involves no change in kinetic energy. There must be no net force on the test charge at all times and the test charge is moved with a constant speed to the target location. Therefore, an equal and oppposite external force is needed to balance the electric force. The work done by the two forces therefore have opposite signs.

The potential is simply this external force integrated from infinity to the target location.

  • $\begingroup$ And when it arrives at the point we need will it repel And go away to infinity $\endgroup$ – Ahmad Eldesokey Sep 10 '18 at 22:39
  • $\begingroup$ @Ahmad Eldesokey: If we stop exerting this force, it will of course go back to infinity and we get back the same amount of work. $\endgroup$ – user7777777 Sep 10 '18 at 22:45
  • $\begingroup$ Why should we move the test charge slowly $\endgroup$ – Ahmad Eldesokey Sep 10 '18 at 22:51
  • 1
    $\begingroup$ @user7777777 All that is required is that the charge starts and finishes with the same speed (kinetic energy). It could move at a large but constant speed to achieve this. $\endgroup$ – Farcher Sep 10 '18 at 23:04
  • $\begingroup$ How the test charge will start to move from infinity if the net force on it is zero $\endgroup$ – Ahmad Eldesokey Sep 11 '18 at 2:04

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