Question: 39: Two point charges -q and +q are placed at a distance of L, as shown in the figure.
The magnitude of electric field intensity at a distance R(R \gg L) varies as:
(1) \frac{1}{R^{4}}
(2) \frac{1}{R^{6}}
(3) \frac{1}{R^{2}}
(4) \frac{1}{R^{3}}
Answer: Option (4)
Explanation:
The given system consists of two equal and opposite point charges +q and -q separated by a small distance L.
Such a system is called an electric dipole.
At a point far away from the dipole, where R \gg L,
the individual electric fields due to the two charges nearly cancel each other,
but a small net electric field remains.
For an electric dipole, the magnitude of the electric field at a distant point varies inversely as the cube of the distance from the dipole.
Mathematically, the electric field of a dipole is proportional to
\frac{1}{R^{3}} when R \gg L.
Hence, the magnitude of electric field intensity varies as \frac{1}{R^{3}}.
Therefore, the correct answer is Option (4).