Electric Dipole And Torque

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Along the axial line of a short electric dipole the field falls off with distance in a characteristic manner, so how does it vary with r?

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The axial field of a short dipole is $E_{axial} = \frac{1}{4\pi\varepsilon_0}\frac{2p}{r^3}$, a result obtained in NCERT Class 12, Chapter 1 (Electric Charges and Fields) by adding the fields of the two charges and taking the limit $r \gg a$. Because the two opposite charges partially cancel, one power of $r$ beyond the single-charge inverse-square behaviour is lost, leaving an inverse-cube dependence. Thus doubling the distance reduces the axial field to one-eighth. The option inverse-square is wrong because that is the behaviour of a single isolated point charge, not a neutral dipole. The option inverse-distance is wrong because that would describe a line charge or a potential, not a dipole field. The option that the field stays constant is wrong because only an idealised infinite sheet produces a distance-independent field, which a dipole is not. It is worth noting the equatorial field of the same dipole also falls as $1/r^3$ but is half the axial value and oppositely directed. A consistency check confirms the cube law: a dipole is charge-neutral overall, so its field must fall faster than a monopole's inverse-square behaviour, and the $1/r^3$ dependence satisfies exactly that physical expectation.

Electric Dipole And Torque

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