Question

three point charges +2MC, -3MC and -3MC are kept at the vertices A, B nad C respectively of an equilateral triangle of side 20 cm as shown in figure. 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

Answer 1

Answer:

Explanation:

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