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Question

A dipole is placed at origin of coordinate system as shown in figure, find the electric field at point P(0,y):

125487_4134c6a5bb3c4695b8783f591212170d.png

A
kPy3(^i2^j)
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B
kPy3(^i+2^j)
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C
kP2y3(^i2^j)
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D
kP2y3(^i+2^j)
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Solution

The correct option is C kP2y3(^i2^j)
The general expression of electric field due to dipole,E=kr3[3(p.^r)^rp] where p= dipole moment.
here, p=Pcos45^iPsin45^j=P2(^i^j),r=y,^r=^j
p.^r=P2(^i^j).^j=P2
therefore, E=kP2y3[3^j^i+^j]=kP2y3[^i2^j]

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