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Question

# A short electric dipole is oriented along +ve x - direction at origin. At which of following point the electric field have no x component ?

A
(1,1,0)
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B
(2,1,0)
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C
(1,2,0)
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D
(1,0,0)
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Solution

## The correct option is C (1,√2,0)Consider a point at a distance r from the origin. Electric field due to dipole P along the direction of position vector ^r, Er=2kPcosθr3 Electric field due to dipole P perpendicular to the direction of position vector ^r i.e. ^θ, Eθ=kPsinθr3 Horizontal component of net electric field, Ex=Ercosθ−Eθsinθ=kPr3[2cos2θ−sin2θ] Ex=kPr3[2−3sin2θ] For the point =(1,√2,0); |^r|=√12+(√2)2=√3 sinθ=√2√3 Hence Ex=0

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