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two point charges one at x=3m and other at x=-3m.A third charge of mass m and charge -Q is released from rest at y=4m. Find the speed of the particle when it reaches the origin

two point charges one at x=3m and other at x=-3m.A third charge of mass m and charge -Q is released from rest at y=4m. Find the speed of the particle when it reaches the origin

Grade:12th pass

1 Answers

Kapil Khare
80 Points
5 years ago
Let the speed of the particle be v when it reaches the origin.
Let the charge of point charges be q.
Uinitial = (-KQq/5) + (-KQq/5) + (Kq2/6)
          = (-2KQq/5) + (Kq2/6)
Ufinal = (-KQq/3) + (-KQq/3) + (Kq2/6) + (mv2/2)
         = (-2KQq/3) + (Kq2/6) + (mv2/2)
We know that,
                                 Uinitial = Ufinal
\implies   (-2KQq/5) + (Kq2/6) = (-2KQq/3) + (Kq2/6) + (mv2/2)
\implies                      (mv2/2) = (2KQq/3) + (-2KQq/5)
\implies                      (mv2/2) = (4KQq/15)
\implies                               v = (8KQq/15m)½
 
Thus speed of particle on reaching origin is (8KQq/15m)½.

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