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Show that work done by a conservative fo...

Show that work done by a conservative force on a particle moving between two points is path independent.

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The force does work on the particle as it moves along each path
`W_("ab, 1")="word done from a to b along path 1"`
`W_("ab, 2")="work done from b to a along path 2"`
If the force is conservative, then the net work done during the round to trip must be zero.
`W_("ab, 1")+W_("ba, 2")" ...(i)"`
Work done along the forward path must be the negative of the work done along the parth back. Let us now consider work, `W_("ab, 2")` work done on the particle moves from a to b along path 2, as shown in figure 18(a). If the force is conservative, then the work is the negative of `W_("ba, 2")`
`W_("ab, 2")=-W_("ba, 2")" ...(ii)"`
From (i), (ii), we get
`W_("ab, 1")=W_("ab, 2")`
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