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Two point charges(+Q) and (-2Q) are fixe...

Two point charges`(+Q)` and `(-2Q)` are fixed on the `X`-axis at position `a` and `2a` from origin respectively. At what position on the axis, the resultant electric field is zero

A

Only `x= sqrt(2)a`

B

Only `x= -sqrt(2)a`

C

Both `x= +-sqrt(2)a`

D

`x=(3a)/(2)`Only

Text Solution

Verified by Experts

The correct Answer is:
B
Suppose electric field is zero at a point `P` lies at a distance `d` from the charge `+Q`.

At `P (kQ)/(d^(2))=(2)/((a+d)^(2))implies d= (a)/((sqrt(2)-1))`
Since `dgta` i.e., point `P` must lies on negative `x`-axis as shown at a distance `x` from origin hence
`x= d-a= (a)/((sqrt(2)-1))-a = sqrt(2)a`.
Actually P lies on negative x-axis so `x =-sqrt(2)a`.
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Knowledge Check

  • Two point charges (+Q) and (-2Q) are fixed on the X-axis at positions a and 2a from origin respectively. At what positions on the axis, the resultant electric field is zero

    A
    Only `x= sqrt(2)a`
    B
    Only `x= -sqrt(2)a`
    C
    Both `x= +-sqrt(2)a`
    D
    `x=(3a)/(2)cm`

  • Point charges + 4q, -q and + 4q are kept on the x- axis at points x = 0, x = a and X = 2a respectively, then

    A
    Only `q` is in stable equilibrium
    B
    None of the charges are in equilibrium
    C
    All the charges are in unstable equilibrium
    D
    All the charges are in stable equilibrium

  • Two point charges +8q and -2q are located at x=0 and x=L respectively. The location of a point on the x axis at which the net electric field due to these two point charges is zero is

    A
    (a) `L/4`
    B
    (b) `2L`
    C
    (c) `4L`
    D
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