Question 813: Electrostats & Capacitance

Question

The electric potential at a point on the axis of an electric dipole is proportional to [r = distance between centre of the electric dipole and the point]

Accepted Answer

For an electric dipole, the potential at a point in space is given by the equation:
$$ V = \frac{1}{4\pi\varepsilon_0} \frac{{\bf p} \cdot \hat{r}}{r^2} $$
where:
$$p$$ is the dipole moment,
$$\hat{r}$$ is the unit vector pointing from the center of the dipole to the point of interest, and
$$r$$ is the distance between the center of the dipole and that point.
On the axis of the dipole, the dipole moment and the unit vector point in the same direction. This means that $$	extbf{p} \cdot \hat{r} = p$$, and the potential simplifies to:
$$ V = \frac{1}{4\pi\varepsilon_0} \frac{p}{r^2} $$
Thus, the electric potential is proportional to $$\frac{1}{r^2}$$.
To summarize in a few steps:
The general dipole potential is $$V = \frac{1}{4\pi\varepsilon_0}\frac{{\bf p}\cdot\hat{r}}{r^2}$$.
On the axis, $$	extbf{p} \cdot \hat{r} = p$$.
So, the potential on the axis becomes $$V = \frac{1}{4\pi\varepsilon_0}\frac{p}{r^2}$$.
Therefore, the potential is proportional to $$\frac{1}{r^2}$$.
The correct answer is Option B: $$\frac{1}{r^2}$$.

Answer

$\frac{1}{\mathrm{r}}$

Answer

$\frac{1}{r^2}$

Answer

$r$

Answer

$\frac{1}{\mathrm{r}^3}$

Electrostats & Capacitance

The electric potential at a point on the axis of an electric dipole is proportional to [r = distance between centre of the electric dipole and the point]

Choose the correct answer: