Question

Find the magnitude of the electric field at the point P in the configuration shown in the figure for d >> a.
Figure

Answer 1

Dipole Moment is at The Equatorial Line

Explanation:

• This is like an electric field due to dipole at the point on the equatorial line. from the fig. we can see that $sin \theta$ components will be cancelled out and $cos \theta$ components will be added up.

$E_{net} = 2 E \times cos \theta$

= $2 \times \frac {kq}{x^2} cos \theta$

= $\frac {2kqa}{x^3}$

= $\frac {2qa}{4 \pi \varepsilon _0(a^2 + r^2)^{(\tfrac{3}{2})}}$

Dipole Moment is Given by -

p = 2qa

$\vec{E} = \frac {\vec{p}}{4 \pi \varepsilon _0(a^2 + r^2)^{(\tfrac{3}{2})}}$