Question

Three electric charges \(2q\), \(2q\), \(-4q\) are placed at the corners of equilateral triangle of side \({}'x'\). The magnitude of electric dipole moment of the system is

• A. \(2qx\)
• B. \(\sqrt{2}qx\)
• C. \(\sqrt{3}qx\)
• D. \(2\sqrt{3}qx\)

Hint:

The net charge is zero, so the dipole moment does not depend on the origin; place the origin at the -4q charge.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept
For a neutral system, the dipole moment is \(\vec{p}=\sum q_{i}\vec{r}_{i}\) and is independent of the chosen origin.

Step 2: Calculation
Put the origin at the \(-4q\) corner. Then \(\vec{p}=2q\vec{r}_{1}+2q\vec{r}_{2}=2q(\vec{r}_{1}+\vec{r}_{2})\), where \(\vec{r}_{1}\) and \(\vec{r}_{2}\) have length \(x\) and are \(60^{\circ}\) apart. So \(|\vec{r}_{1}+\vec{r}_{2}|=2x\cos 30^{\circ}=\sqrt{3}x\).

Step 3: Compare the options
\(p=2q\times\sqrt{3}x=2\sqrt{3}qx\), which is the fourth option.

Final Answer:
The magnitude of the dipole moment is \(2\sqrt{3}qx\). \[ \boxed{\text{(D) }2\sqrt{3}\,qx} \]