Surface tension. Surface tension is the force that causes the surface of water (and other liquids) to form a "skin” that resists penetration. Because of this force, water forms into beads, and insects such as water spiders can walk on water. As we shall see, the force is electric in nature. The surface of a polar liquid, such as water, can be viewed as a series of dipoles strung together in the stable arrangement in which the dipole moment vectors are parallel to the surface, all pointing in the same direction. Suppose now that something presses inward on the surface, distorting the dipoles as shown in Figure 17.48 . Show that the two slanted dipoles exert a net upward force on the dipole between them and hence oppose the downward external force. Show also that the dipoles attract each other and thus resist being separated. Notice that the force between dipoles opposes penetration of the liquid's surface and is a simple model for surface tension. Figure 17.48 Problem 26.
Surface tension. Surface tension is the force that causes the surface of water (and other liquids) to form a "skin” that resists penetration. Because of this force, water forms into beads, and insects such as water spiders can walk on water. As we shall see, the force is electric in nature. The surface of a polar liquid, such as water, can be viewed as a series of dipoles strung together in the stable arrangement in which the dipole moment vectors are parallel to the surface, all pointing in the same direction. Suppose now that something presses inward on the surface, distorting the dipoles as shown in Figure 17.48 . Show that the two slanted dipoles exert a net upward force on the dipole between them and hence oppose the downward external force. Show also that the dipoles attract each other and thus resist being separated. Notice that the force between dipoles opposes penetration of the liquid's surface and is a simple model for surface tension. Figure 17.48 Problem 26.
Surface tension. Surface tension is the force that causes the surface of water (and other liquids) to form a "skin” that resists penetration. Because of this force, water forms into beads, and insects such as water spiders can walk on water. As we shall see, the force is electric in nature. The surface of a polar liquid, such as water, can be viewed as a series of dipoles strung together in the stable arrangement in which the dipole moment vectors are parallel to the surface, all pointing in the same direction. Suppose now that something presses inward on the surface, distorting the dipoles as shown in Figure 17.48. Show that the two slanted dipoles exert a net upward force on the dipole between them and hence oppose the downward external force. Show also that the dipoles attract each other and thus resist being separated. Notice that the force between dipoles opposes penetration of the liquid's surface and is a simple model for surface tension.
Calculate the magnitude and direction of the Coulomb force on each of the three charges shown in Figure P15.10.
-d-
P
+q
b- b-
+q
-
Electric quadrupole. The figure shows an electric quadrupole. It
consists of two dipoles with dipole moments that are equal in
magnitude but opposite in direction. What is the value of E on the
axis of the quadrupole for a point P a distance z from its center
(assume z >> d)? Take Q = 2qd? (which is known as the quadrupole
moment of the charge distribution.)
NOTE: Express your answer in terms of Q and z, using eo when needed.
E =
Note this problem relies on material in section 20.5, some of which we covered in class, and some you
will be expected to read on your own. It is mostly straight forward calculations using the equations
provided in the text. You may, of course, ask questions in class about it, but that will be up to you.
A dipole has dipole moment p = 1.5 x 10-9C-m oriented in the + direction and is in a uniform
electric field of strength Eo = 4.0 x 10 N/C that is directed 30° from the dipole as shown. The axis
perpendicular to the dipole and a test point on that axis are also shown.
Eo
(a) What would the charge separation in this dipole be if it were due to one electron and one proton
(ie a hydrogen atom)? What would the separation be if it were due to charges of ±1nC?
(b) Find the magnitude of the torque on the dipole.
(c) Find the work required to rotate the dipole until it is antiparallel to the field (i.e., until 7 points
in the opposite direction of the electric field).
(d) What would be the…
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