Two positive charges +q1 and +q2 are placed at fixed positions x=a and x=b (b>a>

Question

Two positive charges +q1 and +q2 are placed at fixed positions x=a and x=b (b>a>0) respectively. If a third particle of charge +Q and mass M is brought in from infinity and placed at x = c (for c > b) then: a) How much work was done to bring this third object in from infinity to c? b) If the object is now released and allowed to move under the influence of the other two charges, what will its speed be after it travels a distance d away from c? c) How fast will it be when it gets very far away from the two stationary charges?

Explanation / Answer

a)     Work done by the electro static force on the point charge as the charge moves from infinity to the particular point                  W = U ( potential energy )                       = Q ?V     where    ?V = potential at point C due to point A - potential at point C due to point B   b)        (1 / 2) mv2 = q ?V                           v = v q?V / 2m c) when the charge Q is very far away from the two stationary charges                    potential is zero            ( 1 /2) mv^2 = 0                         velocity of charge Q at infinity is zero                     

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