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Charges 5mC, 4inC and 6mC are placed at the three corners A, B and C respectively of a square ABCD of side X metre. Find, what charge must be places at the fourth corner so that the total potential at the centre of the square is zero. |
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Answer» Solution :`q_1= 2 xx 10^(-6)C, q_2= 4 xx 10^(-6)C, q _3 = 6 xx 10^(-6) C, q_4 =?` AB =BC =CD =DA =X from fig ` AC^2 = AB^2 +BC^2` ` AC^2 =X^2 +x^2` ` AC= sqrt(2) X ` `AO = (sqrt(2))/(2) X=(x )/( sqrt(2)) = BO =CO=DO ` The total electric potential is zero at the centre of the square is `(1)/(4 pi epis_0) [(q_1)/(AO) +(q_2)/(BO) +(q_3)/(CO)]=-(1)/(4 pi epsi_0) [(q_4)/(DO)]` `[(2xx 10^(-6))/((x)/(sqrt(2)))+(4 xx 10^(-6))/((x)/(sqrt(2)))+(6xx 10^(-6))/( (x)/(sqrt(2)))]=-(q_4)/((x)/(sqrt(2)))` ` ( sqrt(2))/(X ) [2 xx 10^(-6) + 4 xx 10^(-6) +6 xx 10^(-6)]=-(sqrt(2))/(X)[q_4]` ` q_4 =- 12 xx 10^(-6) C ` ` q_4=- 12mu C ` 
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