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In electrostatics E=-dV/dR where E=electric field and V=electric potential. Then how can there be E on equtorial axis of an electric dipole where V is zero?

In electrostatics E=-dV/dR where E=electric field and V=electric potential. Then how can there be E on equtorial axis of an electric dipole where V is zero?

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2 Answers

Ashish Gupta IIT Roorkee
askIITians Faculty 12 Points
9 years ago
dV = -\int\overrightarrow{E}.d\overrightarrow{r} = -[Ex dx + Ey dy + Ez dz]
Hence, Er = - dV/dr

On equatorial axis of an electric dipole, electric field in the direction of radius vector i.e. Er = 0 as you can verify that V is 0 on equatorial axis and hence dV/dr = 0.
Electric field is there but it is actually perpendicular to radius vector.
Rishi Sharma
askIITians Faculty 646 Points
3 years ago
Dear Student,
Please find below the solution to your problem.

645-1447_01.PNG

Hence,
645-1943_01.PNG

On equatorial axis of an electric dipole, electric field in the direction of radius vector i.e. Er = 0 as you can verify that V is 0 on equatorial axis and hence [dV/dr = 0] . Electric field is there but it is actually perpendicular to radius vector.

Thanks and Regards

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