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A charge q is placed at the centre of th...

A charge q is placed at the centre of the line joining two equal charges Q. The system of the three charges will be in equilibrium if q is equal to:

A

`Q//2`

B

`-Q//2`

C

`Q//4`

D

`-Q//4`

Text Solution

Verified by Experts

The correct Answer is:
D
Let q charge is situated at themidposition of the lineAB.The distance between AB is x. A and B be the positions of charges Q and Q respectively.

Let `AC = (x)/(2), BC = (x)/(2)`
The force on A due to charge q at C.
`vecF_(CA) = (1)/(4piepsi_(0)). (Q.q)/((x//2)) ` a long `vecAC`
The system is in equilibrium, then two oppositely directed force must be equal,i.e., total force on A is equal to zero.
`vecF _(CA) + vecF_(AB) = 0 rArr vecF_(CA) = - vecF_(AB)`
` (1)/(4piepsi_(0)).(4Q_(q))/(x^(2)) = (-1)/(4piepsi_(0)) , (Q^(2))/(x^(2))`
`rArr q = - (Q)/(4)`
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Knowledge Check

  • If a charge q is placed at the centre of the line joining two equal charges Q such that the system is in equilibrium then the value of q is

    A
    (a) `Q/2`
    B
    (b) `-Q/2`
    C
    (c) `Q/4`
    D
    (d) `-Q/4`

  • A charge q is placed at the center of the line joining two equal charges Q . Three charges are in equilibrium then what will be the value of 'q' ?

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    `(Q)/(4)`
    B
    `(-Q)/(4)`
    C
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    D
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  • Two point charges q_(1) = +2 C and q_(2) = - 1C are separated by a distance d . The position on the line joining the two charges where a third charge q = + 1 C will be in equilibrium is at a distance

    A
    `(d)/(sqrt(2))` from `q_(1)` and `q_(2)`
    B
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    C
    `(d)/(sqrt(2) - 1)` from `q_(2)` between `q_(1)` and `q_(2)`
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