# Four-point

Consider a square of side 10 cm. Four charges are placed in its corners. Let O be the center of the square.

The diagram is:

AB = BC = CD = DA = 10 cm

Diagonal of a square = √2 × Side of a square

Therefore,

AC = BD = 10√2 cm

AO = OC = DO = OB = (10√2)/2 cm = 5√2cm

i. A charge of magnitude 1μC is placed at O, the center of the square.
ii. The force experienced at center due to side charge at B is same in magnitude but in a direction opposite to the direction to the force at center due to charge at D.
iii. The force experienced at center due to side charge at A is same in magnitude but in a direction opposite to the direction to the force at center due to charge at C .

Force on the 1 u C in the center is =  Fa  +   Fb  +  F+  Fd  =  F+ (- Fa) + F+ ( - Fd) = 0

Therefore, we can conclude that the resultant force by the four charges kept in the corners on the charge that is kept in the center will be zero.

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