Two electric dipoles of moment P and 27 P are | vedclass

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(A) Let the point where the electric field is zero be at a distance $x$ from the centre of the dipole with moment $P$. The distance from the dipole wi

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$6$

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(A) Let the point where the electric field is zero be at a distance $x$ from the centre of the dipole with moment $P$. The distance from the dipole with moment $27P$ is $(24 - x)$.For an axial point of a dipole, the electric field magnitude is given by $E = \frac{1}{4 \pi \varepsilon_0} \cdot \frac{2p}{r^3}$.At the point where the net electric field is zero, the magnitudes of the electric fields due to both dipoles must be equal:$\frac{1}{4 \pi \varepsilon_0} \cdot \frac{2P}{x^3} = \frac{1}{4 \pi \varepsilon_0} \cdot \frac{2(27P)}{(24 - x)^3}$$\frac{1}{x^3} = \frac{27}{(24 - x)^3}$Taking the cube root on both sides:$\frac{1}{x} = \frac{3}{24 - x}$$24 - x = 3x$$4x = 24$$x = 6 \,cm$.

Two electric dipoles of moment $P$ and $27 P$ are placed on a line with their centres $24 \,cm$ apart. Their dipole moments are in opposite directions. At which point between the dipoles, measured from the centre of the dipole of moment $P$, will the electric field be zero (in $\,cm$)?

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