The ratio of magnitudes of Electric field strength at A (2,0,0) and at B (2, 23, 0) due to a short dipole having dipole moment p→=i^+3j^ , kept at origin is:

Eax=2kpr3 Eeq=kpr3 here for point (2, 0, 0) ⇒r=2 EA=E1+E2=2k(1)23i^+k(3)23j^ EA=(k4)2+(3k8)2=7k8 EB=k16So, EAEB=27

The ratio of magnitudes of Electric field strength at A (2,0,0) and at B (2, 23, 0) due to a short dipole having dipole moment p→=i^+3j^ , kept at origin is:

Eax=2kpr3 Eeq=kpr3 here for point (2, 0, 0) ⇒r=2 EA=E1+E2=2k(1)23i^+k(3)23j^ EA=(k4)2+(3k8)2=7k8 EB=k16So, EAEB=27

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The ratio of magnitudes of Electric field strength at $A (2, 0, 0)$ and at $B (2, 2 \sqrt{3}, 0)$ due to a short dipole having dipole moment $\vec{p} = \hat{i} + \sqrt{3} \hat{j}$ , kept at origin is:

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$8 \sqrt{7}$

$2 \sqrt{7}$

$\frac{\sqrt{7}}{8}$

answer is C.

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Detailed Solution

$E_{ax} = \frac{2 kp}{r^{3}} E_{eq} = \frac{kp}{r^{3}} here for point (2, 0, 0) \Rightarrow r = 2 E_{A} = E_{1} + E_{2} = \frac{2 k (1)}{2^{3}} \hat{i} + \frac{k (\sqrt{3})}{2^{3}} \hat{j} E_{A} = \sqrt{{(\frac{k}{4})}^{2} + {(\frac{\sqrt{3} k}{8})}^{2}} = \frac{\sqrt{7} k}{8}$