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.

An electric dipole with dipole moment $p$ is in a uniform external electric field $E$. Show that for the stable orientation in part (b), the dipole's own electric field tends to oppose the external field. Note: Part (b) asked which of the orientations in part (a) is stable, and which is unstable? (Hint: Consider a small rotation away from the equilibrium position and see what happens.) Also, part (a) asked to find the orientations of the dipole for which the torque on the dipole is zero.

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.

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?

An electric dipole with dipole moment $p$ is in a uniform external electric field $E$. Which of the orientations in part (a) is stable, and which is unstable? (Hint: Consider a small rotation away from the equilibrium position and see what happens.) Note: Part (a) asked to find the orientations of the dipole for which the torque on the dipole is zero.

A very long, straight wire has charge per unit length $3.20\times {10}^{-10}$ C/m. At what distance from the wire is the electric field magnitude equal to $2.50$ N/C?

A charge of $-6.50$ nC is spread uniformly over the surface of one face of a nonconducting disk of radius $1.25$ cm. Why is the field in part (a) stronger than the field in part (b)? Why is the field in part (c) the strongest of the three fields? Note: Part (a) asked to find the magnitude and direction of the electric field this disk produces at a point $P$ on the axis of the disk a distance of $2.00$ cm from its center. Part (b) asked to find the magnitude and direction of the electric field at point $P$, supposing that the charge were all pushed away from the center and distributed uniformly on the outer rim of the disk. Part (c) asked to find the magnitude and direction of the electric field at point $P$ if the charge is all brought to the center of the disk.