Find the magnitude of the electric field at points along the axis of a dipole (along the same line that contains +Q and −Q) for

Question

Anon25

1 month ago

8

Find the magnitude of the electric field at points along the axis of a dipole (along the same line that contains +Q and −Q) for

r≫ℓ, where r is the distance from a point to the center of the dipole and ℓ is the distance between +Q and −Q.

Physics

1 answer:

ValentinkaMS [3.4K] · Answer 1 · 2026-03-06T13:06:02+03:00

Response:

E= $\frac{2K\cdot P}{r^3}$

Clarification:

We have a dipole consisting of charges Q and -Q, separated by distance l. If a charge of +1 C is positioned at point P at a distance r from the dipole's center, we need to find the strength of the electric field along the dipole's axis.

We know that the Electric field is defined as $\frac{Force}{unit \;positive\;Charge}$

The electric field due to the positive charge Q is represented as $E_1=\frac{kQ}{(r+\frac{\rho}{2})^2}$ (pointing from A to P).

The electric field produced by the negative charge -Q is given as $E_2=\frac{KQ}{(r-\frac{\rho}{2})^2}$ (towards PB).

The total electric field can be expressed as E= $E_2-E_1$

E= $\frac{kQ}{(r-\frac{\rho}{2})^2}-\frac{KQ}{(r+\frac{\rho}{2})^2}$

E= $KQ\frac{r^2+\rho^2+r\rho-r^2-\rho^2+r\rho}{(r^2-\frac{\rho^2}{4})^2}$

E= $\frac{2 KQ r\rho}{(r^2-\frac{\rho^2}{4})^2}$

In circumstances where r is much larger than L, we can say that E= $\frac{2KQ r\rho}{r^4}=\frac{2kQ \rho}{r^3}$

E= $\frac{K\cdot 2Q\rho}{r^3}$

E= $\frac{2K\cdot P}{r^3}$

Where P represents the dipole, which is the distance between the two charges, and $\times$ represents any charge.