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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?

Grade:

2 Answers

Ashish Gupta IIT Roorkee
askIITians Faculty 12 Points
6 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
10 months 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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