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CBSE Class 12-science Answered

Prove that work done by an electric field in path independent
Asked by elizabethcordilia1997 | 04 Apr, 2019, 09:07: PM
answered-by-expert Expert Answer
Potential energy Va at a point a  in electric field is defined as the workdone to bring a unit positive charge from infinity to that point
 
Va = begin mathsize 12px style negative integral subscript negative infinity end subscript superscript a E open parentheses r close parentheses d r end style  ............................(1)
Similarly Potential energy Vb at a point b is given by, Vb = begin mathsize 12px style negative integral subscript negative infinity end subscript superscript b E left parenthesis r right parenthesis d r end style  .......................(2)
Hence potential difference between a and b is obtained by finding the difference of eqn(1) and eqn.(2),
 
  Va - Vb  = begin mathsize 12px style integral subscript a superscript b E left parenthesis r right parenthesis d r end style  .............................(3)
RHS of eqn.(3) is workdone to move a unit positive charge from point a to point b in electric field.
 
LHS of eqn.(3) is potential energy difference. 
 
Hence from eqn.(3), we conclude, workdone to move a positive charge from a point to another point in electric field
is only the potential energy difference between those points and independent of path of moving
Answered by Thiyagarajan K | 05 Apr, 2019, 11:02: AM

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