Three identical dipoles are arranged as shown below. What will be…

MCQ

Three identical dipoles are arranged as shown below. What will be the net electric field at $P$ $\left( {k = \frac{1}{{4\pi {\varepsilon _0}}}} \right)$

A
$\frac{{k.p}}{{{x^3}}}$
B
$\frac{{2kp}}{{{x^3}}}$
✓
Zero
D
$\frac{{\sqrt 2 \,kp}}{{{x^3}}}$

✓

Answer

Correct option: C.

Zero

c
(c) Point $P$ lies at equatorial positions of dipole $1$ and $2$ and axial position of dipole $3$.
Hence field at $P$
due to dipole $1$
${E_1} = \frac{{k.p}}{{{x^3}}}$ (towards left)
due to dipole $2$
${E_2} = \frac{{k.p}}{{{x^2}}}$ (towards left)
due to dipole $3$ ${E_3} = \frac{{k.(2p)}}{{{x^3}}}$ (towards right)
So net field at $P$ will be zero.

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