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IT si required to hold four equal point ...

IT si required to hold four equal point charges each having a charge `Q=(8)/(7)(1-2sqrt(2))C` in equilibrium at the corners of a square.Find the point charge in coulombs that will do this if placed at the centre of the square.

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The correct Answer is:
2
Let us the consider the equilibrium of charge `Q` placed at `2`.Then for equilibrium
`vec(F_(2))=vec(0)rArr vec(F)_(2x)hat(i)+F_(2y)hat(j)=0rArr F_(2x)=0`
`rArr F_(21)+F_(24)cos45^(@) +F_(25)cos45+F_(23)cos90=0`
`rArr (Q)/(4piepsilon_(0)a^(2))+(Q)/(4piepsilon_(0)(sqrt(2a)^(2)))+(Q)/(4piepsilon_(0)((a)/(sqrt(2)))^(2))(1)/(sqrt(2))+0=0`
`rArr Q+(Q)/(2sqrt(2))+sqrt(2q)=0`
` rArr Q(2sqrt(2)+1)+4q=0rArr q=-(Q)/(4)(2sqrt(2)+1)`
since `Q=(8)/(7)(1-2sqrt(2))`
`rArr q=-(1)/(4)[(8)/(7)(1-2sqrt(2))+(1+2sqrt(2))]`
`rArr q=-(1)/(4)((8)/(7))(-7)=2C`
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