Two electric dipoles of moment P and 8P are p | vedclass

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Question

(A) The electric field due to a dipole of moment $p$ at a distance $r$ on its axis is $E = \frac{2kp}{r^3}$.For two dipoles of moments $p_1$ and $p_2$

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$2$

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(A) The electric field due to a dipole of moment $p$ at a distance $r$ on its axis is $E = \frac{2kp}{r^3}$.For two dipoles of moments $p_1$ and $p_2$ placed at a distance $d$ apart in opposite directions, the electric field is zero at a point $x$ from $p_1$ if $\frac{2kp_1}{x^3} = \frac{2kp_2}{(d-x)^3}$.This simplifies to $\frac{x}{d-x} = \left(\frac{p_1}{p_2}ight)^{1/3}$, which gives $x = \frac{d \cdot p_1^{1/3}}{p_1^{1/3} + p_2^{1/3}}$.Case $1$: $p_1 = P, p_2 = 8P, d = 24 	ext{ cm}$.$x_1 = \frac{24 \cdot P^{1/3}}{P^{1/3} + (8P)^{1/3}} = \frac{24}{1 + 2} = \frac{24}{3} = 8 	ext{ cm}$.Case $2$: $p_1 = P, p_2 = 27P, d = 24 	ext{ cm}$.$x_2 = \frac{24 \cdot P^{1/3}}{P^{1/3} + (27P)^{1/3}} = \frac{24}{1 + 3} = \frac{24}{4} = 6 	ext{ cm}$.Difference $|x_2 - x_1| = |6 - 8| = 2 	ext{ cm}$.

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