Two particles A and B having charges ` 8.0 xx 10 ^(-6) C` and `-2.0 xx 10(-6) C` respectively are held fixed with a. separtion of 20cm. Where should a thired charged. particle be placed so that it dose not experience a net electric force?.

Explanation

For equilibrium `vecF_(AC)+vecF_(CB)=0 `
Let the charge at point c is theta
` (qtheta)/(4piepsilon_0x^2)+(2qtheta)/(4piepsilon_0(d-x)^2)=0 `
` Again vecF_(AC) = vecF_(CB) `
` So, 1/x^2=2/(d-x)^2 `
` or 2x^2=(d-x)^2 `
` or sqrt2x=d-x `
` x=(sqrt2-1)d `
` For charge at rest `
` vecF_(AC) = vecF_(CB) `
` 1/(4piepsilon_0)xx(qtheta) /[(sqrt2-1)d^2]+1/(4piepsilon_0)(qxx2q)/d^2=0 `
` or theta = (6-4sqrt2)q`.