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.

Explanation

`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 =- 12 mu C `