Question

Two point dipoles \(p\hat{k}\) and \(\frac{p}{2}\hat{k}\) are located at \((0,0,0)\) and \((1\,\text{m},0,2\,\text{m})\) respectively. The resultant electric field due to the two dipoles at the point \((1\,\text{m},0,0)\) is:

• A. \(\dfrac{9p}{32\pi\varepsilon_0}\hat{k}\)
• B. \(-\dfrac{7p}{32\pi\varepsilon_0}\hat{k}\)
• C. \(\dfrac{7p}{32\pi\varepsilon_0}\hat{k}\)
• D. None of these

Hint:

Always check whether the point lies on axial or equatorial line of a dipole.

Answer 1

The Correct Option is A

Step 1: Electric field of a dipole on its axial line: \[ E = \frac{1}{4\pi\varepsilon_0}\frac{2p}{r^3} \]
Step 2: Calculate fields due to both dipoles at the given point and add vectorially.
Step 3: Resultant field is along \(\hat{k}\) direction with magnitude: \[ E = \frac{9p}{32\pi\varepsilon_0} \]