Question

An electric dipole consists of charges \(\pm 4 \mu C\) separated by a distance of \(6\,cm\). Calculate the electric field at a point on the axial line at a distance \(20\,cm\) from its center.

Hint:

The electric field on the axial line of a dipole is directed along the dipole moment and decreases with cube of the distance from the center.

Answer 1

Step 1: Use the formula for electric field on axial line of dipole: \[ E = \frac{1}{4\pi\varepsilon_0} \cdot \frac{2p}{r^3} \] Where: \[ p = q \cdot 2a = 4 \times 10^{-6} \cdot 0.06 = 2.4 \times 10^{-7} \, C\cdot m \\ r = 0.20\, m, \quad \frac{1}{4\pi\varepsilon_0} = 9 \times 10^9 \, Nm^2/C^2 \] \[ E = 9 \times 10^9 \cdot \frac{2 \cdot 2.4 \times 10^{-7}}{(0.2)^3} = 9 \times 10^9 \cdot \frac{4.8 \times 10^{-7}}{8 \times 10^{-3}} = 9 \times 10^9 \cdot 6 \times 10^{-5} = 5.4 \times 10^5 \, N/C \] Final Answer:
\[ \boxed{E = 5.4 \times 10^5 \, \text{N/C (along dipole axis)}} \]