Question

Obtain the formula for the intensity of electric field on the equatorial point of an electric dipole.

Hint:

The electric field at the equatorial position is directed opposite to the dipole moment.

Answer 1

Step 1: Consider an electric dipole consisting of charges \( +q \) and \( -q \) separated by a distance \( 2a \). The dipole moment is: \[ \vec{p} = q \cdot 2a \] Step 2: The electric field at an equatorial point (perpendicular bisector) of the dipole at a distance \( r \) from the center is given by the formula: \[ E_{\text{equatorial}} = \frac{1}{4 \pi \varepsilon_0} \cdot \frac{p}{(r^2 + a^2)^{3/2}} \] Step 3: For large distances (\( r \gg a \)): \[ E_{\text{equatorial}} \approx \frac{1}{4 \pi \varepsilon_0} \cdot \frac{p}{r^3} \] \[ \boxed{E = \frac{1}{4 \pi \varepsilon_0} \cdot \frac{p}{r^3}} \]