Question

9. As a simple model of surface tension, the surface of a polar liquid, like water, can be viewed as a series of dipoles strung together in a stable arrangement in which the dipole moment vectors are parallel to the surface and all point in the same direction. Suppose that something presses inward on the surface, distorting the dipoles as shown below (a) Show, qualitatively, that the two slanted dipoles exert a net upward force on the dipole between them, and the downward external force. (b) Also show that adjacent dipoles attract each other and therefore resist being separated. A water strider uses surface tension to walk on water.

Answer 1

a)

The two slanted dipoles exert a force R on the central dipole. Let the force R makes an angle Theta with the horizontal, then the horizontal forces R cos theta exerted by two slanted dipoles on central dipole cancel each other. The two vertical forces R sin theta exerted by two slanted dipoles on central dipole add up to make 2 R sin theta, which acts vertically upwards on central dipole. Hence 2 R sin theta opposes the downward external force� F The positive charge on left most dipole attracts the negative charge on central dipole . The negative charge on right most dipole attracts the positive charge on central dipole. The left dipole pulls the central dipole with a force R towards left, and the right dipole pulls the central dipole with a force R towards right. So the central dipole cannot move either to left or to right as equal forces are acting on it in two opposite directions. Hence the adjacent dipoles attract each other, and cannot be separated.

The two slanted dipoles exert a force $R$ on the central dipole. Let the force $R$ makes an angle $\theta$ with the horizontal, then the horizontal forces $R\cos\theta$ exerted by two slanted dipoles on central dipole cancel each other. The two vertical forces $R\sin\theta$ exerted by two slanted dipoles on central dipole add up to make $2R\sin\theta$ , which acts vertically upwards on central dipole.

Hence $2R\sin\theta$ opposes the downward external force $F$ .

b)

The positive charge on left most dipole attracts the negative charge on central dipole . The negative charge on right most dipole attracts the positive charge on central dipole.

The left dipole pulls the central dipole with a force $R$ towards left , and the right dipole pulls the central dipole with a force $R$ towards right. So the central dipole cannot move either to left or to right as equal forces are acting on it in two opposite directions.

Hence the adjacent dipoles attract each other, and cannot be separated.