# Two charges $\pm 10 \mu C$ are placed $5.0$ mm apart.Determine the electric field at a point Q, 15 cm away from O on a line passing through O and normal to the axis of the dipole, as shown in Fig.

Field at Q due to charge $+ 10 \mu C$ at B
$\qquad= \large\frac{10^{-5}\;C}{4 \pi (8.854 \times 10^{-12} C^{2} N^{-1} m^{-2})} \times \large\frac{1}{[15^2+(0.25)^2] \times 10^{-4} m^2}$
$\qquad= 3.99 × 10^6\; N C^{–1}$ along BQ
Field at Q due to charge $–10\; \mu \;C$ at $A$
$\qquad= \large\frac{10^{-5}\;C}{4 \pi (8.854 \times 10^{-12} C^{2} N^{-1} m^{-2})} \times \large\frac{1}{[15^2+(0.25)^2] \times 10^{-4} m^2}$
$\qquad= 3.99 × 10^6\; N C^{–1}$ along QA
Clearly, the components of these two forces with equal magnitudes cancel along the direction OQ but add up along the direction parallel to BA. Therefore, the resultant electric field at Q due to the two charges at A and B is
$\qquad= 2 \times \large\frac{0.25 }{\sqrt {15^2 +(0.25)62 } }$$\times 3.99 \times 10^6 \;NC^{-1}$ along BA
$\qquad= 1.33 \times 10^5 \;NC^{-1}$
The direction of electric field in this case is opposite to the direction of the dipole moment vector. Again the result agrees with that obtained before.
Hence C is the correct answer.
answered Jun 2, 2014 by