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The point charges + q, 2q and + q are pl...

The point charges `+ q, 2q` and `+ q` are placed at point `(x = 0, y = a, z = 0), (x = 0, y = 0, z = 0)` and `(x = a, y = 0, z = 0)`, repectively. The magnitude and direction of the electric dipole moment vector of this charge assembly are

A

`sqrt2 qa` along + y direction

B

`sqrt2 qa` along the line joining points
`(x = 0, y = 0, z = 0)` and `(x = a, y = a, z = 0)`

C

`aq` along the line joining points
`(x = 0, y = 0, z =0)` and `(x = a, y = a, z = 0)`

D

`sqrt2 qa` along + x direction

Text Solution

Verified by Experts

The correct Answer is:
B
(b) Electric dipole moment is a vector quantity directed from negative charge to the similar positive charge. Choose the three corrdinate axes as `x, y` and `z` and plot the charges with the given coordinates as shown.
`O` is the origin at which `- 2q` charge is placed is placed. The system is equivalent to two diploes along `x` and y-directions respecitvely. The dipole moments of two dipolmes are shown in figure.
The resultant dipole moments will be directed along `OP` where `P = (a, a, 0)`. The magnitude of resultant dipole moment is
`p' = sqrt(p^(2) + p^(2))`
`= sqrt((qa)^(2) + (qa)^(2)) = sqrt(2) qa`
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Knowledge Check

  • Three point charges +q, -2q and +q are placed at points (x = 0, y = a, z = 0), (x = 0, y = 0, z = 0) and (x = a, y = 0, z = 0), respectively. The magnitude and direction of the electric dipole moment vector of this charge assembly are

    A
    `sqrt2`qa along +y direction
    B
    `sqrt2`qa along the line joining points
    (x = 0, y = 0, z = 0)
    and (x = a, y = a, z = 0)
    C
    qa along the line joining points
    (x = 0, y = 0, z = 0)
    and (x = a, y = a, z = 0)
    D
    `sqrt2`qa along +x direction

  • Three point charges +q, -2q and +q are placed at points (x = 0, y = a, z = 0), (x = 0, y = 0, z = 0) and (x = a, y = 0, z = 0), respectively. The magnitude and direction of the electric dipole moment vector of this charge assembly are

    A
    `sqrt2`qa along +y direction
    B
    `sqrt2`qa along the line joining points
    (x = 0, y = 0, z = 0)
    and (x = a, y = a, z = 0)
    C
    qa along the line joining points
    (x = 0, y = 0, z = 0)
    and (x = a, y = a, z = 0)
    D
    `sqrt2`qa along +x direction

  • Three point charges +q, –2q and +q are placed at points (x = 0, y = a, z = 0), (x = 0,y = 0, z = 0) and (x = a, y = 0, z = 0) respectively. The magnitude and direction of the electric dipole moment vector of this charge assembly are:-

    A
    `sqrt(2)` qa along + x direction
    B
    `sqrt(2)` qa along + y direction
    C
    `sqrt(2)` qa along the line joining points (x=0,y=0,z=0) and (x=a,y=a,z=0)
    D
    qa along the line joining points (x=0,y=0,z=0) and (z=a , y=a ,z=0)

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