Point charges q1=-4.5 nC and q2=+4.5 nC are separated by 3.1 mm, forming an electric dipole. (a)

step 1 So here we're given the magnitude of the charges and the distance between them, which is what we

Point charges q1=-4.5 nC and q2=+4.5 nC are separated by 3.1...

Point charges $q_{1}=-4.5 \mathrm{nC}$ and $q_{2}=+4.5 \mathrm{nC}$ are separated by 3.1 mm, forming an electric dipole. (a) Find the electric dipole moment (magnitude and direction). (b) The charges are in a uniform electric field whose direction makes an angle of $36.9^{\circ}$ with the line connecting the charges. What is the magnitude of this field if the torque exerted on the dipole has magnitude $7.2 \times 10^{-9} \mathrm{N} \cdot \mathrm{m} ?$

Point charges $q_{1}=-4.5 \mathrm{nC}$ and $q_{2}=+4.5 \mathrm{nC}$ are separated by 3.1 mm, forming an electric dipole. (a) Find the electric dipole moment (magnitude and direction). (b) The charges are in a uniform electric field whose direction makes an angle of $36.9^{\circ}$ with the line connecting the charges. What is the magnitude of this field if the torque exerted on the dipole has magnitude
$7.2 \times 10^{-9} \mathrm{N} \cdot \mathrm{m} ?$

Key Concepts

Torque on an Electric Dipole

When an electric dipole is placed in a uniform electric field, it experiences a torque that tends to align the dipole with the field. The magnitude of this torque is given by the product of the dipole moment, the strength of the electric field, and the sine of the angle between the dipole moment and the electric field. This concept is important for understanding how dipoles interact with external fields, as it explains the rotational forces acting on the dipole.

Electric Dipole Moment

The electric dipole moment is a vector quantity that represents the separation of positive and negative charges. Its magnitude is defined as the product of one of the charge magnitudes and the distance between the charges, and its direction is conventionally taken from the negative charge to the positive charge. This concept is central to understanding the behavior of pairs of charges in external electric fields and forms the basis for analyzing the interaction of dipoles with electric fields.

Uniform Electric Field

A uniform electric field is characterized by having the same magnitude and direction at every point in the region it occupies. This simplification allows for straightforward calculations of forces and torques acting on charges or dipoles within the field. In the context of dipole analysis, it facilitates the use of fixed angle relationships and constant field strength when determining the effects on the dipole’s orientation and dynamics.

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