Question 839: Electrostats & Capacitance

Question

If $$\mathrm{E}_{\mathrm{a}}$$ and $$\mathrm{E}_{\mathrm{q}}$$ represent the electric field intensity due to a short dipole at a point on its axial line and on the equatorial line at the same distance '$$r$$' from the centre of the dipole, then

Accepted Answer

To solve this problem, we need to understand the electric field intensity due to a short dipole at two specific points: on the axial line and on the equatorial line.
For a short dipole, the expressions for the electric field intensity are as follows:
1. On the axial line (line extending along the dipole axis):
$$ \mathrm{E}_{\mathrm{a}} = \frac{1}{4 \pi \epsilon_0} \cdot \frac{2 p}{r^3} $$
where $$p$$ is the dipole moment, $$r$$ is the distance from the center of the dipole, and $$\epsilon_0$$ is the permittivity of free space.
2. On the equatorial line (line perpendicular to the dipole axis at the center):
$$ \mathrm{E}_{\mathrm{q}} = \frac{1}{4 \pi \epsilon_0} \cdot \frac{p}{r^3} $$
Notice the difference in the coefficients. The electric field on the axial line is twice as strong as that on the equatorial line at the same distance $$r$$.
Thus, the relationship between $$\mathrm{E}_{\mathrm{a}}$$ and $$\mathrm{E}_{\mathrm{q}}$$ can be derived:
Given:
$$ \mathrm{E}_{\mathrm{a}} = 2 \mathrm{E}_{\mathrm{q}} $$
Therefore, the correct option is:
Option D
$$\mathrm{E}_{\mathrm{a}} = 2 \mathrm{E}_{\mathrm{q}}$$

Answer

$$\mathrm{E}_{\mathrm{a}}=\mathrm{E}_{\mathrm{q}}$$

Answer

$$\mathrm{E}_{\mathrm{a}}=\frac{1}{2} \mathrm{E}_{\mathrm{q}}$$

Answer

$$\mathrm{E}_{\mathrm{a}}=\frac{1}{\sqrt{2}} \mathrm{E}_{\mathrm{q}}$$

Answer

$$\mathrm{E}_{\mathrm{a}}=2 \mathrm{E}_{\mathrm{q}}$$

Electrostats & Capacitance

If $\mathrm{E}_{\mathrm{a}} and \mathrm{E}_{\mathrm{q}} represent the electric field intensity due to a short dipole at a point on its axial line and on the equatorial line at the same distance 'r$' from the centre of the dipole, then

Choose the correct answer: