question_answer

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)         \[\frac{1}{{{r}^{4}}}\]

E)  \[\frac{1}{{{r}^{6}}}\]

Correct Answer: C

Solution :

For a dipole of length\[2l\] \[E=\frac{1}{4\pi {{\varepsilon }_{0}}K}.\frac{2pr}{{{({{r}^{2}}-{{l}^{2}})}^{2}}}\] When\[(l<<r),\]then\[{{l}^{2}}\]may be neglected in comparison to\[{{r}^{2}}\]. \[\therefore \]  \[E=\frac{1}{4\pi {{\varepsilon }_{0}}K}\frac{2pr}{{{r}^{4}}}=\frac{1}{4\pi {{\varepsilon }_{0}}K}=\frac{2p}{{{r}^{3}}}N/C\] \[\Rightarrow \]               \[E\propto \frac{1}{{{r}^{3}}}\]