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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?

A

`-(q)/(2)(1+2sqrt(2))`

B

`(q)/(2)(1+2sqrt(2))`

C

`-(q)/(4)(1+2sqrt(2))`

D

`-(q)/(4)(1+2sqrt(2))`

Text Solution

Verified by Experts

The correct Answer is:
D
`AC=sqrt(21)=BD`
or,`BO=(1)/(sqrt(2))`

`F_(BO)=F_(BD)+(F_(BA)+F_(BC)) cos 45^(@)`
Solving we get
`Q=(q)/(4)(1+2sqrt(2))` Q should be negative of q.
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