24. Electric Force & Field; Gauss' Law

Torque on a Dipole. An electric dipole with dipole moment p is in a uniform external electric field E. (c) Show that for the stable orientation in part (b), the dipole's own electric field tends to oppose the external field.

Torque on a Dipole. An electric dipole with dipole moment p is in a uniform external electric field E. (b) 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.)

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

Point charges q1 = -4.5 nC and q2 = +4.5 nC are separated by 3.1 mm, forming an electric dipole. (b) 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 * 10^-9 N•m?

An electric dipole consists of two opposite charges ±q separated by a small distance s. The product p=qs is called the dipole moment. FIGURE P22.61 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.

The permanent electric dipole moment of the water molecule (H₂O) is 6.2×10^−30 C m . What is the maximum possible torque on a water molecule in a 5.0×10^8 N/C electric field?

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, p⃗ =αE⃗ , where α is called the polarizability of the molecule. A bigger field stretches the molecule farther and causes a larger dipole moment. b. An ion with charge q is distance r from a molecule with polarizability α . Find an expression for the force Ē ion on dipole .

The electric field strength 1.5 cm from an electric dipole, on the axis of the dipole, is 1.5×10^5 N/C. c. If the dipole is replaced by a single charge, what magnitude charge in nC will give the same field strength 1.5 cm away?