Question

At great distances from an electric dipole, the electric field strength due to the dipole varies with the distance as

• A. $\frac{1}{r}$
• B. $\frac{1}{r^2}$
• C. $\frac{1}{r^3}$
• D. $\frac{1}{r^4}$

Hint:

The electric field of a dipole falls off as $1/r^3$, unlike a point charge which falls off as $1/r^2$.

Answer 1

The Correct Option is C

The problem at hand involves understanding how the electric field strength due to an electric dipole varies with distance from the dipole. Let’s analyze this step by step:

Concept of Electric Dipole:

An electric dipole consists of two equal and opposite charges separated by a small distance. The dipole moment, denoted by \(p\), is given by the product of the charge value \(q\) and the separation distance \(d\), i.e., \(p = q \cdot d\).

Electric Field Due to a Dipole:

At a point along the axial line of the dipole, the electric field \(E\) at a distance \(r\) from the center of the dipole is given by the expression:

\(E = \frac{1}{4\pi\epsilon_0} \cdot \frac{2p}{r^3}\)

Similarly, at a point along the equatorial line of the dipole, the electric field \(E\) is:

\(E = \frac{1}{4\pi\epsilon_0} \cdot \frac{p}{r^3}\)

In both expressions, we can observe that the field varies inversely with \(r^3\). This explains the behavior of the field at large distances from the dipole.

Conclusion:

Thus, the electric field strength due to a dipole at large distances from it varies as \(\frac{1}{r^3}\), making the correct option \(\frac{1}{r^3}\).

Rule Out Other Options:

• The option \(\frac{1}{r}\) is incorrect because it represents the field variation of a very different scenario, such as potential at a distance.
• The option \(\frac{1}{r^2}\) pertains to the electric field due to a point charge, not a dipole.
• The option \(\frac{1}{r^4}\) may relate to other complex situations but is not applicable for a simple electric dipole.