Question

Obtain an expression for the electric field due to an electric dipole at a point on the line passing through the centre of the dipole and perpendicular to the dipole axis

Answer 1

Field Intensity on Equatorial position of dipole:

$\rm E_{net}= 2E \cos( \theta)$

• This is because the sine components will be cancelled.

$\rm \implies E_{net}= 2 \times \dfrac{kq}{ {d}^{2} } \times \dfrac{l}{d}$

$\rm \implies E_{net}= 2 \times \dfrac{kq}{ {( \sqrt{ {r}^{2} + {l}^{2} } )}^{2} } \times \dfrac{l}{ \sqrt{ {r}^{2} + {l}^{2} } }$

$\rm \implies E_{net}= 2 \times \dfrac{kq}{ {r}^{2} + {l}^{2} } \times \dfrac{l}{ \sqrt{ {r}^{2} + {l}^{2} } }$

$\rm \implies E_{net}= \dfrac{2kql}{ {({r}^{2} + {l}^{2})}^{ \frac{3}{2} } }$

$\rm \implies E_{net}= \dfrac{kP}{ {({r}^{2} + {l}^{2})}^{ \frac{3}{2} } }$

• 'P' = 2ql .

When r >>> l , we can say:

$\rm \implies E_{net}= \dfrac{kP}{ {r}^{3} }$

Hope It Helps !