First slide

Electric dipole

Question

An electric dipole of moment $\vec{p_{1}} = p \hat{i}$ is placed at the origin and the electric field at point. A(r, o) is found to be E.Now another electric dipole of moment $\vec{p_{2}} = p \hat{j}$ is placed at the origin. Then the resultant electric field at point A will be

Moderate

A

$\sqrt{\frac{2}{5}} E$
B

$\sqrt{\frac{5}{2}} E$
C

$\frac{\sqrt{5}}{2} E$
D

$\frac{\sqrt{2}}{5} E$

Solution

$\begin{array}{l} E_{1} = \frac{1}{4 π \in_{0}} \frac{2 p_{}}{r^{3}} = E \\ E_{2} = \frac{1}{4 π \in_{0}} \frac{p}{r^{3}} \end{array} ∴ E_{R} = \sqrt{E_{1}^{2} + E_{2}^{2}} = \sqrt{5} \cdot \frac{1}{4 π \in_{o}} \frac{p}{r^{3}} \Rightarrow E_{R} = \frac{\sqrt{5}}{2} E$

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