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Q2.Three point charges of +2 micro coulomb,-3 micro coulomb and -3 micro coulomb are kept at the vertices A,B & C respectively of an equilateral triangle of side 20 cm.What should be the sign and magnitude of the charge to be placed at the midpoint ,m of side BC ,so that the charge at A remains at equilibrium.

Solution: The forces on the charge at A due to the charges at B and C are equal in magnitude and are given by 
These are directed as in the figure shown above. Their resultant is given 
and is directed along AM. 
Suppose, a charge +q is placed at M for the equilibrium of the charge at A. 
The force on the charge at A due to the charge q is given by 
But (AM)2 = (AB)2 - (BM)2 = (0.2m)2 - (0.1m)2
                       =  0.03m2 
The force F1 is directed as shown. For the equilibrium of the charge at A, we must have 
F1 = F12 


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