Question
Tue March 03, 2015 By: Ankur Pandey

how does potential energy of (1)mutual interection (2)net electrostatic potencial energy of two charges change when they are placed in an external electric field.

Expert Reply
Priyanka Kumbhar
Tue March 03, 2015
begin mathsize 14px style Let space straight q subscript 1 and space straight q subscript 2 space be space two space point space charges space at space position space vectors space stack straight r subscript 1 with rightwards arrow on top space and space space stack straight r subscript 2 with rightwards arrow on top space respectively space placed space in space external space electric space field. Let space work space done space by space charge space straight q subscript 1 space end subscript bringing space it space from space infinity space to space position space space stack straight r subscript 1 with rightwards arrow on top space against space electric space field space be space straight W subscript 1 space equals straight q subscript 1 space end subscript. straight V space left parenthesis stack straight r subscript 1 with rightwards arrow on top right parenthesis. space Where space space straight V space left parenthesis stack straight r subscript 1 with rightwards arrow on top right parenthesis space be space the space potential. Similarly comma space Let space work space done space by space charge space straight q subscript 2 space end subscript bringing space it space from space infinity space to space position space space stack straight r subscript 2 with rightwards arrow on top space against space electric space field space be space straight W subscript 2 space equals space straight q subscript 2. straight V space left parenthesis stack straight r subscript 2 with rightwards arrow on top right parenthesis. space Where space space straight V space left parenthesis stack straight r subscript 2 with rightwards arrow on top right parenthesis space be space the space potential. As space straight q subscript 2 space is space bringing space from space infinity space to space position space stack straight r subscript 2 with rightwards arrow on top comma space their space is space also space work space has space to space be space done space against space the space field space due space to space straight q subscript 1 Hnece comma space due space to space mutual space interaction space between space two space charges space work space done space is space straight W subscript 12 space equals space fraction numerator straight q subscript 1 straight q subscript 2 over denominator 4 straight pi element of subscript 0 straight r subscript 12 end fraction apostrophe space whre space straight r subscript 12 space be space the space distance space between space straight q subscript 1 space end subscript and space straight q subscript 2 The space net space electrostatic space potential space energy space is space equal space to space total space work space done space in space assembling space the space configuration space straight U space equals space straight W subscript 1 space plus space straight W subscript 2 space plus space straight W subscript 12 rightwards double arrow space straight U space equals space straight q subscript 1 space end subscript. straight V space left parenthesis stack straight r subscript 1 with rightwards arrow on top right parenthesis space plus space straight q subscript 2. straight V space left parenthesis stack straight r subscript 2 with rightwards arrow on top right parenthesis space plus space fraction numerator straight q subscript 1 straight q subscript 2 over denominator 4 straight pi element of subscript 0 straight r subscript 12 end fraction end style
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