When we consider the interaction between an electric dipole and an infinite line of charge, it's essential to understand the nature of electric fields and forces. An electric dipole consists of two equal and opposite charges separated by a small distance. When this dipole is placed in an electric field, it experiences forces that can lead to both translational motion and rotational motion, depending on the orientation of the dipole relative to the field.
Understanding the Electric Field of a Line Charge
An infinite line of charge creates a uniform electric field around it. The direction of this electric field is radially outward from the line if the line charge is positive, and inward if it is negative. The strength of the electric field (E) at a distance (x) from the line charge can be expressed as:
where λ is the linear charge density and ε₀ is the permittivity of free space. This electric field is perpendicular to the line of charge and decreases with distance from the line.
Behavior of the Electric Dipole
When the dipole is oriented perpendicular to the line of charge, each charge of the dipole experiences a force due to the electric field. The positive charge of the dipole will experience a force in the direction of the electric field, while the negative charge will experience a force in the opposite direction. This results in a net force that pulls the dipole toward the line of charge.
Force and Torque on the Dipole
In this scenario, the dipole not only experiences a force but also a torque because of the difference in forces acting on the two charges. The torque tends to align the dipole with the electric field. However, the primary effect here is the translational force that attracts the dipole toward the line of charge.
Conclusion on the Interaction
Given this analysis, the correct statement regarding the dipole's behavior when placed perpendicular to an infinite line of charge is:
- (a) The dipole is attracted towards the line charge.
This attraction occurs due to the differential forces acting on the two charges of the dipole, leading to a net force directed toward the line of charge. Thus, option (a) accurately describes the situation.
