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

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

A

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

B

`(Q)/(4)(1+2sqrt(2))`

C

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

D

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

Text Solution

Verified by Experts

The correct Answer is:
B
If all charges are in equilibrium, system system is also in equilibrium
Charge at center is in equilibrium because no net force is acting on it.

At corner B, charge is in equilibrium,
if `F_(AC)+F_(D)=F_(O)`
`implies (sqrt(2)KQ^(2))/(a^(2))+(KQ^(2))/((sqrt(2)a)^(2))=(KqQ)/((a//sqrt(2))^(2))`
`implies (KQ^(2))/(a^(2))[sqrt(2)+(1)/(2)]=(2KqQ)/(a^(2))`
`implies Q(sqrt(2)+(1)/(2))=2qimpliesq=(Q(sqrt(2)+(1)/(2)))/(2)`
`=(Q)/(4)(2sqrt(2)+1)`.
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