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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.

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Solution

## Given: Magnitude of charge, q = 2.0 × 10−6 C Separation between the charges, l = 1.0 cm (a) Dipole moment, P = q × l $P=2×{10}^{-6}×{10}^{-2}\phantom{\rule{0ex}{0ex}}=2×{10}^{-8}\mathrm{C}-\mathrm{m}$ (b) Electric field at the axial point of the dipole, $E=\frac{1}{4\mathrm{\pi }{\epsilon }_{0}}\frac{2P}{{r}^{3}}\phantom{\rule{0ex}{0ex}}E=\frac{9×{10}^{9}×2×2×{10}^{-8}}{{\left(0.01\right)}^{3}}$ E = 36 × 107 N/C (c) Electric field at at a point on the perpendicular bisector of the dipole, $E=\frac{1}{4\mathrm{\pi }{\epsilon }_{0}}\frac{P}{r{\text{'}}^{3}}\phantom{\rule{0ex}{0ex}}E=\frac{9×{10}^{9}×2×{10}^{-8}}{{1}^{3}}$ E = 180 N/C

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