In Section 22.3 we claimed that a charged object exerts a net attractive force on an electric dipole. Let's investigate this. FIGURE CP22.80 shows a permanent electric dipole consisting of charges +q and −q separated by the fixed distance s. Charge +Q is distance r from the center of the dipole. We'll assume, as is usually the case in practice, that s≪r. Use the binomial approximation $(1+x{)}^{-n}\approx 1-nx$ if x≪1 to show that your expression from part a can be written $F_{net}=2KqQs/r^3$.

An electric dipole with dipole moment $p$ is in a uniform external electric field $E$. Find the orientations of the dipole for which the torque on the dipole is zero.

Point charges $q_1=-4.5$ nC and $q_2=+4.5$ nC are separated by $3.1$ mm, forming an electric dipole. The charges are in a uniform electric field whose direction makes an angle of $36.9$° with the line connecting the charges. What is the magnitude of this field if the torque exerted on the dipole has magnitude $7.2\times {10}^{-9}$ Nm?

The dipole moment of the water molecule (H₂O) is $6.17\times {10}^{-30}$ Cm. Consider a water molecule located at the origin whose dipole moment $p$ points in the $+x$-direction. A chlorine ion (Cl^-), of charge $-1.60\times {10}^{-19}$ C, is located at $x=3.00\times {10}^{-9}$ m. Find the magnitude and direction of the electric force that the water molecule exerts on the chlorine ion. Is this force attractive or repulsive? Assume that $x$ is much larger than the separation $d$ between the charges in the dipole, so that the approximate expression for the electric field along the dipole axis derived in Example $21.14$ can be used.

An electric dipole consists of two opposite charges $\pm q$ separated by a small distance $s$. The product $p=qs$ is called the dipole moment. Figure P$22.61$ shows an electric dipole perpendicular to an electric field $E$. Find an expression in terms of $p$ and $E$ for the magnitude of the torque that the electric field exerts on the dipole.

An electric dipole is formed from two charges, ±q, spaced 1.0 cm apart. The dipole is at the origin, oriented along the y-axis. The electric field strength at the point (x, y)=(0 cm, 10 cm) is 360 N/C. What is the charge q? Give your answer in nC.

The permanent electric dipole moment of the water molecule (H₂O) is $6.2\times {10}^{-30}$ Cm. What is the maximum possible torque on a water molecule in a $5.0\times {10}^8$ N/C electric field?

Derive Equation 23.11 for the field Ē dipole in the plane that bisects an electric dipole.

An electric field can induce an electric dipole in a neutral atom or molecule by pushing the positive and negative charges in opposite directions. The dipole moment of an induced dipole is directly proportional to the electric field. That is, $\overrightarrow{p}=\alpha \overrightarrow{E}$, where α is called the polarizability of the molecule. A bigger field stretches the molecule farther and causes a larger dipole moment. An ion with charge q is distance r from a molecule with polarizability α. Find an expression for the force _{$\overrightarrow{E}$ion on dipole}.