Question

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.

Answer 1

Answer:

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

Explanation:

We are given that a dipole consist of two charge Q and -Q and charge separated by l.Let a charge +1 C is placed at  point P at distance r from the centre of dipole.

We have to find the magnitude of the electric field at point along the axis of dipole .

We know that Electric field=$\frac{Force}{unit \;positive\;Charge}$

Electric filed due to positive charge Q

$E_1=\frac{kQ}{(r+\frac{\rho}{2})^2}$ {from A to P}

Electric field due to negative charge -Q

$E_2=\frac{KQ}{(r-\frac{\rho}{2})^2}$ ( Along PB)

Net electric field 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=$\frac{2 KQ r\rho}{(r^2-\frac{\rho^2}{4})^2}$

We are given that r >> L then

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=Diple = Distance between two charges $\times$ any charge