Question

Two particles A and B, of opposite charges 2.0 × 10⁻⁶ C and −2.0 × 10⁻⁶ C, are placed at a separation of 1.0 cm. (a) Write down the electric dipole moment of this pair. (b) Calculate the electric field at a point on the axis of the dipole 1.0 cm away from the centre. (c) Calculate the electric field at a point on the perpendicular bisector of the dipole and 1.0 m away from the centre.

Answer 1

Given:
Magnitude of charge, q = 2.0 × 10⁻⁶ C
Separation between the charges, l = 1.0 cm

(a) Dipole moment, P = q × l
$$\begin{gathered} P=2\times {10}^{-6}\times {10}^{-2} \\ =2\times {10}^{-8}\mathrm{C}-\mathrm{m} \end{gathered}$$

(b) Electric field at the axial point of the dipole,
$$\begin{gathered} E=\frac{1}{4\mathrm{\pi }{\epsilon }_0}\frac{2P}{r^3} \\ E=\frac{9\times {10}^9\times 2\times 2\times {10}^{-8}}{{\left(0.01\right)}^3} \end{gathered}$$
E = 36 × 10⁷ N/C

(c) Electric field at at a point on the perpendicular bisector of the dipole,
$$\begin{gathered} E=\frac{1}{4\mathrm{\pi }{\epsilon }_0}\frac{P}{r{\text{'}}^3} \\ E=\frac{9\times {10}^9\times 2\times {10}^{-8}}{1^3} \end{gathered}$$
E = 180 N/C