Question

If $\overrightarrow{E_{ax}}$ and $\overrightarrow{E_{eq}}$ represents electric field at a point on the axial and equatorial line of a dipole. If points are at a distance $r$ from the centre of the dipole, for $r\gg a$:

• A. $\overrightarrow{E_{ax}}=\overrightarrow{E_{eq}}$
• B. $\overrightarrow{E_{ax}}=-\overrightarrow{E_{eq}}$
• C. $\overrightarrow{E_{ax}}=-2\overrightarrow{E_{eq}}$
• D. $\overrightarrow{E_{eq}}=2\overrightarrow{E_{ax}}$

Answer 1

Answer: (C)

$\overrightarrow{E_{ax}}=-2\overrightarrow{E_{eq}}$

Electric field on axial line of dipole is given by:

${\overrightarrow{E}}_{ax}=\frac{2\overrightarrow{p}}{4\pi {\epsilon }_o{r}^3}$ for $r>>a$

Electric field on equatorial line of dipole is given by:

${\overrightarrow{E}}_{ax}=-\frac{\overrightarrow{p}}{4\pi {\epsilon }_o{r}^3}$ for $r>>a$

$⟹{\overrightarrow{E}}_{ax}=-2{\overrightarrow{E}}_{eq}$