I am having some problem with the formulas for calculating the electric fields of an infinite line of charge and an electric dipole. I don't understand conceptually why they are the way they are. Can someone explain? Any help is appreciated!(adsbygoogle = window.adsbygoogle || []).push({});

[Note: K=1/(4*pi*epsilon_o), lambda=linear charge density, p=electric dipole moment, E=electic field, r is the distance]

Point charge:

E=Kq/r^2 <---the electric field falls off as 1/r^2.

Infinite line of charge:

E=K(2 lambda)/r <---the field falls off as 1/r, i.e. falls off slower than that of a point charge as you move further away.

Electric dipole:

E=K(2p)/r^3 (field on axis)

E=-Kp/r^3 (field in bisecting plane)

<---the field falls off as 1/r^3, i.e. falls off faster than that of a point charge as you move further away.

Now, is there any easy way toexplainthe distance-dependence of the electric field of the electric dipole and infinite line of charge? (the colored part above) Why do the formulas make sense? What actually determines the rate at which the electric field falls off as you move away from the charge?

Thank you for explaining!:)

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# Electric fields of infinite line & electric dipole

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