Electric Dipole

A dipole is a separation of positive and negative charges, and can be represented as a pair of point charges, with opposite charges.

Moment §

Let $d$ be the distance between two point charges, $A$ and $B$, with charge $+q$ and $-q$ respectively. Then the dipole Moment is defined as:

Electric Dipole Moment

$${\vec{\mu }}_E=q\vec{d}$$

Note

• ${\vec{\mu }}_E\text{ or }\vec{p}$ = Dipole moment vector, pointing from negative to positive charge (in $\text{Cm}$)
• $\vec{d}$ = Displacement Vector between $A$ and $B$ (in $\text{m}$)
• $q$ = Magnitude of Charge on $A$ and $B$ (in $\text{C}$)

Electric Field (Along X and Y Axis) §

Y Axis §

$${\vec{E}}_Y=k_e\times (\frac{q}{{\left(y-\frac{d}{2}\right)}^2}+\frac{-q}{(y+\frac{d}{2}{)}^2})$$

$$=q\times k_e\times \frac{2yd}{(y+\frac{d}{2}{)}^2(y-\frac{d}{2}{)}^2}$$

However, if the distance from the dipole, $y$ is much greater than $d$, we can safely ignore $d$.

$${\vec{E}}_Y=q{k}_e\times \frac{2yd}{y^4}=k_e\times q\times \frac{2d}{y^3}=\frac{2k_{e}qd}{y^3}$$

Recall that the electric dipole moment $\vec{p}$ is given by:

$$\vec{p}=qd$$

$${\vec{E}}_Y=\frac{2\vec{p}\times k_e}{y^3}$$

X Axis §

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