Torque on a Dipole An electric dipole consists of charges +2...

Torque on a Dipole An electric dipole consists of charges $+2 e$ and $-2 e$ separated by $0.78 \mathrm{~nm}$. It is in an electric field of strength $3.4 \times 10^{6} \mathrm{~N} / \mathrm{C}$. Calculate the magnitude of the torque on the dipole when the dipole moment is (a) parallel to, (b) perpendicular to, and (c) antiparallel to the electric field.

Key Concepts

Electric Dipole

An electric dipole consists of two equal and opposite charges separated by a distance. It serves as a basic model in electromagnetism to study how systems with separated charges interact with electric fields, providing insight into phenomena from molecular polarity to the behavior of antennas.

Electric Dipole Moment

The electric dipole moment is a vector quantity defined as the product of one of the charges and the distance vector pointing from the negative to the positive charge. It characterizes the strength and orientation of the dipole, and it plays a central role in determining how the dipole interacts with external electric fields.

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 moment with the field. The magnitude of this torque is given by the cross product of the dipole moment and the electric field, mathematically expressed as ? = pE sin?, where ? is the angle between the dipole moment and the electric field.

Angle Dependence in Torque

The magnitude of the torque on a dipole in an electric field depends on the sine of the angle between the dipole moment and the field direction. This means that the torque is zero when the dipole is either parallel or antiparallel to the field (? = 0° or 180°), and it reaches its maximum value when the dipole is perpendicular to the field (? = 90°).

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