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Four charges equal to -Q are placed at t...

Four charges equal to `-Q` are placed at the four corners fo a square and a charge `q` is at its centre, If the system is in equilibrium the value of `q` si

A

`-Q/4(1+2sqrt2)`

B

`Q/4(1+2sqrt2)`

C

`-Q/2(1+2sqrt2)`

D

`Q/2(1+2sqrt2)`

Text Solution

Verified by Experts

The correct Answer is:
B
The system is in equilibrium net force on any charge will be zero. Consider any corner’s charge
Resultant of all three forces is `(sqrt2 kQ^2)/a^2+(kQ^2)/(sqrt2 a)^2`
The must be balanced by attraction of charge at centre
`(kQq)/((1/2 sqrt2a))= (kQq)/(a^2//2)`
On solving we get `(2kQq)/a^2= (sqrt2 kQ^2)/a^2+(kQ^2)/(2a^2)`
`2q=sqrt2 Q+Q/2 implies q=Q/sqrt2 +Q/4 (1/sqrt2+1/4)=Q/4(1+2sqrt2)`
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