Question

Figure shows two dipole moments parallel to each other and placed at a distance x apart x is very large. Then:

• A. they will repel each other
• B. they will attract each other
• C. force of interaction is of magnitude of $\frac{3P_1P_2}{4\pi\epsilon_0x^4}$
• D. force of interaction is of magnitude of $\frac{6P_1P_2}{4\pi\epsilon_0x^4}$

Answer 1

Answer: (A), (C)

Options (A) and (C).

Answer 2

For two dipoles with moments $P_1$ and $P_2$ both pointing upward and arranged side-by-side (separated horizontally by a large distance $x$), the interaction energy is given by

$$U = \frac{1}{4\pi\epsilon_0} \frac{P_1P_2}{x^3}.$$

Taking the derivative with respect to $x$, we get the force:

$$F = -\frac{dU}{dx} = \frac{3P_1P_2}{4\pi\epsilon_0x^4}.$$

Since the force is positive (repulsive) along the line joining them, the dipoles repel each other.