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Two charges q and -3q are placed fixed o...

Two charges `q` and `-3q` are placed fixed on x-axis separated by distance `d`. Where should a third charge `2q` be placed such that it will not experience any force ?

A

`(d-sqrt3d)/2`

B

`(d+sqrt3d)/2`

C

`(d+3d)/2`

D

`(d-3d)/2`

Text Solution

Verified by Experts

The correct Answer is:
B

Let a charge 2q be placed at P, at a distance l from A where charge q is placed, as shown in figure.
The charge 2q will not experience any force, when force of repulsion on it due to q is balanced by force of attraction on it due to -3q at B where AB = d
`or" "((2q)(q))/(4piepsilon_(0)l^(2))=((2q)(3q))/(4piepsilon_(0)(l+d)^(2))`
`(l+d)^(2)=3l^(2)or2l^(2)-2ld-d^(2)=0`
`therefore" "l=(2dpmsqrt(4d^(2)+8d^(2)))/4=d/2pm(sqrt3d)/2rArrl=(d+sqrt3d)/2`
If charge 2q is placed between A and B then `l=(sqrt3-1)/2d`
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