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Question

# A short dipole is placed at origin of coordinate system in x-y plane as shown in figure. Find the electric field at point P(0, y). (y>> length of dipole)

A
Kp2y3[2ˆiˆj]
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B
2Kpy3[2ˆiˆj]
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C
2Kpy3[ˆi2ˆj]
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D
Kp2y3[ˆi2ˆj]
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Solution

## The correct option is D Kp√2y3[−ˆi−2ˆj]We can resolve that dipole moment into two components: along x and y directions respectively. Dipole moment along x-axis, px=pcos45o=p√2 Dipole moment along y- axis, py=psin45o=p√2 Component of electric field parallel to x-axis at point P, →EPx=−Kpxˆiy3=−Kpˆi√2y3 Component of electric field parallel to y-axis at point P, →EPy=−2KPy^jy3=−2Kpˆj√2y3 Net electric field at point P, →Enet=→EPx+→EPy Substituting the values of →EPx and →EPy in the above equation, we get →Enet=Kp√2y3[−ˆi−2ˆj] Hence, option (d) is the correct answer.

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