Question

Two point-charges $ \pm 10\mu C $ are placed $ 5.00\,mm $ apart, forming an electric dipole. Compute electric field at a point on the axis of the dipole $ 15\,cm $ away from the centre on a line passing through the centre dipole.

• A. $ 1.66\times {{10}^{5}}N{{C}^{-1}} $
• B. $ 3.66\times {{10}^{5}}N{{C}^{-1}} $
• C. $ 2.66\times {{10}^{-5}}N{{C}^{-1}} $
• D. $ 2.66\times {{10}^{5}}N{{C}^{-1}} $

Answer 1

Answer: (C)

The magnitude of the electric dipole moment is
$ p=q\times 2l=(10\times 10^{-6})\times (5.00\times 10^{-3}) $
$ =50\times 10^{-9}\,cm $
The field is required at point far-away from the centre of the dipole.
The electric field at an axial point (end-on position) distant $ r(=15\,cm) $ from the centre of the dipole is
$ E=\frac{1}{4\pi \,\varepsilon }_{0}\frac{2p}{r^{3}}=(9.0\times 10^{9})\frac{2\times (50\times 10^{-9})}{(15\times 10^{-2})^{3}} $
$2.66 \times 10^5NC ^{-1}$