A small rigid object carries positive and negative 3.50 -nC...

A small rigid object carries positive and negative 3.50 -nC charges. It is oriented so that the positive charge has coordinates $(-1.20 \mathrm{mm}, 1.10 \mathrm{mm})$ and the negative charge is at the point $(1.40 \mathrm{mm},-1.30 \mathrm{mm} \text { ). (a) Find the electric }$ dipole moment of the object. The object is placed in an electric field $\mathbf{E}=(7800 \hat{\mathbf{i}}-4900 \hat{\mathbf{j}}) \mathrm{N} / \mathrm{C}$ . (b) Find the torque acting on the object. (C) Find the potential energy of the object-field system when the object is in this orientation. (d) If the orientation of the object can change, find the difference between the maximum and minimum potential energies of the system.

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Key Concepts

Electric Dipole Moment

An electric dipole moment is a measure of the separation of positive and negative charges, defined as the product of one of the charges and the displacement vector between the charges. It is a vector quantity that influences how the dipole interacts with external electric fields.

Torque on an Electric Dipole

The torque on an electric dipole in an external electric field is generated by the tendency of the dipole to align with the field. This torque is computed as the cross product of the dipole moment and the electric field, and it determines the rotational effect experienced by the dipole.

Potential Energy of an Electric Dipole

The potential energy of an electric dipole in an electric field is given by the negative dot product of the dipole moment and the electric field. This relationship reflects how the energy of the dipole depends on its orientation relative to the field, with minimum energy achieved when the dipole aligns with the field.

Uniform Electric Field

A uniform electric field is one in which the magnitude and direction remain constant at all points in space. This simplification allows for direct calculation of forces, torques, and potential energies acting on charges and dipoles, making it a fundamental concept in electrostatics.

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