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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 +2sqrt2)`

B

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

C

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

D

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

Text Solution

Verified by Experts

The correct Answer is:
B

Charge `q` to `O` is in equilibrium .
For `-W` to be in equilibrium, we see charge at `C` .
`:. F_("net") on- Q (at C)= 0`
or `(kQ^2)/((sqrt 2a)^2) + (sqrt 2 kQ^2)/a^2 - (kQq)/((a//sqrt 2 )^2) =0`
`:. q = Q/4 (1 + 2 sqrt 2)` .
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