Two tiny electric dipoles of dipole moments P | vedclass

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Question

(B) The electric field $E$ produced by a dipole of moment $P_1$ at a distance $r$ on its axial line is given by $E = \frac{2 K P_1}{r^3}$.The potentia

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$\frac{6 K P_1 P_2}{r^4}$

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(B) The electric field $E$ produced by a dipole of moment $P_1$ at a distance $r$ on its axial line is given by $E = \frac{2 K P_1}{r^3}$.The potential energy $U$ of a dipole $P_2$ in this electric field is $U = -P_2 E = -P_2 \left( \frac{2 K P_1}{r^3} \right) = -\frac{2 K P_1 P_2}{r^3}$.The force $F$ between the dipoles is given by the negative gradient of the potential energy with respect to distance $r$:$F = -\frac{dU}{dr} = -\frac{d}{dr} \left( -\frac{2 K P_1 P_2}{r^3} \right)$.$F = 2 K P_1 P_2 \frac{d}{dr} (r^{-3}) = 2 K P_1 P_2 (-3 r^{-4}) = -\frac{6 K P_1 P_2}{r^4}$.The magnitude of the force is $|F| = \frac{6 K P_1 P_2}{r^4}$.

Two tiny electric dipoles of dipole moments $P_1$ and $P_2$ are placed at a distance $r$ coaxially. Find the magnitude of the electrostatic force between them.

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