Dipole Moment Practice Problems

An electric dipole is an assembly of two equal opposite charges separated by a distance d. When placed in an electric field, the dipole has one stable orientation and the torque on that dipole for that orientation is zero. Does the dipole's electric field point in the same direction as the external electric field or oppose it?

Alignments that offer zero torque when a dipole lies in an even external electric field are classified as stable and unstable. Identify the stable and unstable alignments. Hint: What is the effect of a slight rotation for an equilibrium alignment?

Two tiny charged spheres charged to +q = +3.2 nC and -q = -3.2 nC are connected using a 4.2 mm long non-conducting rod to form an electric dipole. The arrangement is placed in a uniform electric field. The angle made by the electric field and the connecting rod is 40°. If the torque on the dipole is 6.3 × 10^-9 N•m, determine the magnitude of the electric field. Treat the tiny spheres like point charges.

A group of students construct an electric dipole using two small charged spheres. The dipole is placed in a region where the electric field is uniform. What alignments create zero torque on the dipole? 

A dipole is formed by two charges, q1 and -q1, spaced by a fixed distance d. The dipole is positioned as shown in the figure. Additionally, a charge q₂ is located at a distance y from the center of the dipole. Determine the expression of the net force exerted by q₂ on the dipole. Assume y is significantly greater than d. To simplify calculations, you can use the binomial approximation (1 + x)^-n ≈ 1 - nx when x is much smaller than 1.

Derive the expression for the electric field strength E of a dipole in the far field along the bisecting plane in terms of the dipole moment 'p', and the distance r from the dipole.

An ion with a positive charge Q is located at a distance d from a molecule with polarizability α. The ion generates an electric field (E) that induces an electric dipole in the molecule, resulting in the separation of positive and negative charges within the molecule. The magnitude of the induced dipole moment can be expressed as p = αE. Derive an expression for the force, Fion, exerted by the ion on the induced dipole. The expression should be in terms of the charge Q, distance d, polarizability α, and other relevant constants.

Two equal but opposite charges, separated by a small distance, lie on the x-axis. The electric field at a point on the x-axis, 30.0 mm from the midpoint of the two charges, has a magnitude of 3.6 × 10⁴ N/C. Calculate the magnitude of the dipole moment.

Two opposite and equal electric charges are placed on the x-axis, separated by a distance of 2.5 mm, to form an electric dipole. The center of the dipole is placed at the origin of the xy-axis. The magnitude of the electric field at point A (x_A= 13 cm, y_A= 0 cm) from the dipole's center is 3.5 × 10⁵ N/C. Determine the magnitude of the electric charges, in μC.

A molecule of HCl has a permanent electric dipole moment of 3.5 × 10 ⁻³⁰ C•m. The molecule is exposed to a uniform electric field of strength 1.8 × 10⁸ N/C. Determine the maximum torque that the electric field can exert on the HCl molecule.

An electric dipole is formed by two point charges of equal magnitude but opposite signs, ±q, separated by a distance s. The dipole is placed in a uniform electric field E at an angle θ with respect to the direction of the field. Determine an expression for the torque on the dipole in terms of dipole moment p and electric field E.

An electric dipole consists of point charges +q and -q. At a point on its axis, 2.3 cm from the center, the electric field strength is 7.3 × 10⁷ N/C. Calculate the charge Q (in μC) needed for a single charge to produce the same field strength at a distance of 2.3 cm.

The graph below represents the potential energy of an electric dipole formed by two charges, +q and -q, separated by a distance of d. The charges oscillate between ±36°. Calculate the mechanical energy of the dipole.

A CO molecule has a dipole moment of about 1.1×10⁻²⁹ C·m. The two atoms are separated by a distance of about 1.2×10⁻¹⁰ m. (i) What is the net charge on each atom? (ii) Is this equal to an integral multiple of e? If not, explain.