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Four charges of +q, +q, +q and +q are placed at the corners A, B, C and D of a square of side a. Find the resultant force on the charge at D. |
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Answer» Solution :Let SIDE = `a, BD= SQRT(2)a` Along AD force `F_1= 1/(4 pi epsilon_0)cdot (q^2)/(a^2)` Along CD force `F_2 = 1/(4 pi epsilon_0) cdot (a^2) :. F_1 = F_2` Along AD force `F_1 = 1/(4 pi epsilon_0) cdot (q^2)/(a^2) "" :. F_1 = F_2` RESULTANT of `F_1` and `F_2 = sqrt((F_1^2) + F_2^2)) = sqrt(2) .F_1` Force along BD `F_3 = 1/(4 pi epsilon_0) cdot (q^2)/((sqrt(2)a)^2) = 1/2 1/(4 pi epsilon_0) (q^2)/(a^2)` Resultant force at `D = sqrt(2) F_1 + F_3` `= sqrt(2) 1/(4 pi epsilon_0) cdot (q^2)/(a^2) + 1/2 1/(4 pi epsilon_0) cdot (q^2)/(a^2)` `= 1/(4 pi epsilon_0) (q^2)/(a^2) [ sqrt(2) + ½] = (q^2)/(8 pi epsilon_0 a^2) cdot [1 + 2sqrt(2)]` 
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