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Question

A point negative charge Q is placed at a distance r from a dipole with dipole moment P in the x-y plane as shown in figure

The x-component of force acting on the charge Q is

A

2PkQr3cosθ^i

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B
2PkQr3cosθ ^i
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C

PkQrcosθ^i

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D

PkQrcosθ^i

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Solution

The correct option is A

2PkQr3cosθ^i


Resolve components of dipole moment P along the x-axis as shown in the figure.


Electric field due to the component Pcosθ at distance r,

E1=2kPcosθr3^i

Electric field due to the component Psinθ,

E2=kPsinθr3(^j)

Since charge Q is on the axial line at distance r.

So, the force, Fx, along the x-axis on charge Q will be only due to Pcosθ component of dipole moment which is

Fx=QE1

Substituting the value of E1,

Fx=2PkQr3cosθ^i

Hence, option (c) is the correct option.


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