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Four equal point charges, each of magnit...

Four equal point charges, each of magnitude `+Q`, are to be placed in equilibrium at the corners of a square. What should be the magnitude and sign of the point charge that should be placed at the center of the square to do this job?

Text Solution

Verified by Experts

The correct Answer is:
`3.54xx10^(-6)C`
`F_(3)=F_(2)+2F_(1) cos 45^(@)`
.
or `(kqQ)/((1//sqrt(2))^(2))=(kQ Q)/((sqrt(2)l)^(2))+2(kQ Q)/(l^2)(1)/(sqrt(2))`
`q=(Q(2 sqrt(2)+1))/(4)`
Q should be negative as there is attraction between Q and q. So,
`q=(-Q(2 sqrt(2)+1))/(4)` .
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Knowledge Check

  • It is requird to hold four equal point charges +q in equilibrium at the corners of a square. Find the point charge that will do this, if placed at the centre of the square.

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    A
    `(1/(4piepsilon_0))(q/a)^2`
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    C
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