Derive an expression for the intensity of the electric field at a point on the equatorial plane of an electric dipole.

Question

Accepted Answer

>

> [!TLDR]
> On the equatorial line, the perpendicular field components cancel and the axial ones add, giving $E = \dfrac{p}{4\pi\varepsilon_0 (r^2+a^2)^{3/2}}$, which reduces to $\dfrac{p}{4\pi\varepsilon_0 r^3}$ for $r\gg a$, directed opposite to the dipole moment.
>
> **Setup (NCERT/CBSE electric-charges-and-fields):**
> A dipole consists of charges $+q$ and $-q$ separated by $2a$; its dipole moment is $p = q(2a)$, directed from $-q$ to $+q$. Consider a point P on the **equatorial plane** — the perpendicular bisector of the dipole axis — at distance $r$ from the centre O.
>
> **Step 1 — distance from each charge to P:**
> Each charge is at distance
> $$r' = \sqrt{r^2 + a^2}$$
> from P.
>
> **Step 2 — magnitude of each field:**
> The fields due to $+q$ and $-q$ have equal magnitudes:
> $$E_{+} = E_{-} = \frac{1}{4\pi\varepsilon_0}\frac{q}{(r^2+a^2)}$$
> $E_+$ points away from $+q$, $E_-$ points toward $-q$.
>
> **Step 3 — resolve into components:**
> Resolve each field into a component **parallel to the dipole axis** and a component **perpendicular to it** (along OP).
> - The perpendicular (along-OP) components are equal and opposite, so they **cancel**.
> - The components **parallel to the axis** (pointing from $+q$ toward $-q$, i.e. anti-parallel to $\vec{p}$) **add up**. Each contributes a factor $\cos	heta$, where $\cos	heta = \dfrac{a}{\sqrt{r^2+a^2}}$.
>
> **Step 4 — net field:** …

Q.Derive an expression for the intensity of the electric field at a point on the equatorial plane of an electric dipole.

Concept understanding — Electric Dipole in a Field

Electric Dipole in a Uniform Field — First Look

What happens? Two forces, one twist

The torque formula

What does this mean physically?

Q.Derive an expression for the intensity of the electric field at a point on the equatorial plane of an electric dipole.

🎓Unlock everything free for 14 days

Unlock everything free for 14 days