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(C) The electric field due to a dipole of moment $\vec{p}$ at a distance $x$ on its equatorial line is $\vec{E}_{eq} = -\frac{k\vec{p}}{x^3}$.The elec

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(C) The electric field due to a dipole of moment $\vec{p}$ at a distance $x$ on its equatorial line is $\vec{E}_{eq} = -\frac{k\vec{p}}{x^3}$.The electric field due to a dipole of moment $\vec{p}$ at a distance $x$ on its axial line is $\vec{E}_{ax} = \frac{2k\vec{p}}{x^3}$.For the two vertical dipoles, point $M$ lies on their equatorial line. Each produces an electric field of magnitude $\frac{kp}{x^3}$ directed to the left. Thus, the total field from these two is $\frac{kp}{x^3} + \frac{kp}{x^3} = \frac{2kp}{x^3}$ directed to the left.For the horizontal dipole, point $M$ lies on its axial line. It produces an electric field of magnitude $\frac{2kp}{x^3}$ directed to the right.The net electric field at $M$ is the vector sum of these fields: $\vec{E}_{net} = \frac{2kp}{x^3} (	ext{right}) - \frac{2kp}{x^3} (	ext{left}) = 0$.

Three identical dipoles are arranged as shown below. What will be the net electric field at $M$?

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