Question

A dipole withour angular momenturn can simply rotate to align with the field (though i would oscillate uniess it could shed energy). One with angular momentum cannot. Why?

Short answer

A dipole with no angular momentum can simply align itself with the field because it reaches a state of minimum energy this way. One with angular momentum will continue to rotate, despite the presence of the field, due to the conservation of angular momentum. The continued rotation means that the dipole will precess around the field direction rather than aligning with it.

Step-by-step solution

Understanding Dipoles and Magnetic Fields

A dipole in a magnetic field will always try to align itself with the field. This is because when the dipole aligns with the field, the system reaches a state of minimum potential energy. This principle applies to both an electric dipole in an electric field and a magnetic dipole in a magnetic field.

The Role of Angular Momentum

Angular momentum is a measure of the amount of rotation an object has. It is a conserved quantity, meaning it will not change unless an external torque acts on it. In the context of a dipole in a magnetic field, it means that if a dipole had angular momentum before entering the field, it will keep spinning even after it enters the field.

Energy Dissipation

Now imagine a dipole with no angular momentum. It could simply align with the magnetic field, reaching a state of minimum energy. If any oscillations occur during this process,friction-like effects could dissipate energy, and the dipole would eventually come to rest, perfectly aligned with the field.

Dipoles with Angular Momentum

However, if the dipole had nonzero angular momentum, things are different. Because of the conservation of angular momentum, the dipole cannot simply stop rotating and align with the field. This continuous rotation means that the angle between the dipole and the magnetic field periodically changes, causing the dipole to precess around the direction of the magnetic field.

Key concepts

Angular Momentum

Angular momentum is a fundamental concept that describes the rotation of an object. Think of it like an object's tendency to keep spinning. For a dipole, having angular momentum means it's already in motion, spinning around a certain axis. This is a key factor because angular momentum is a conserved quantity, meaning it doesn't just disappear.

• If an object has angular momentum, it will continue spinning at the same rate and direction unless acted upon by an outside force.
• In a magnetic field, a dipole with angular momentum can't just stop and line up with the field instantly, it keeps on spinning.

This is important because even in a new environment—like entering a magnetic field—the dipole's inherent spin won't just vanish. The dipole's rotation affects how it interacts with the magnetic field and prevents it from simply aligning without any precession or change to its angular state.

Magnetic Field

A magnetic field is a region where magnetic forces can be experienced by objects with magnetic properties. It's like an invisible web pulling or orienting magnets and magnetic dipoles towards itself. In the context of this exercise, when a magnetic dipole enters a magnetic field, it seeks to align itself in a particular way—the direction that minimizes potential energy.

• This alignment is because a system always "prefers" to be in a state of lower energy. Think of it like water flowing to the lowest point; energy systems do something similar.
• A dipole without angular momentum will naturally turn and face the direction of the magnetic field lines.

However, once there's angular momentum at play, this natural alignment doesn't occur straightforwardly. The magnetic field tries to influence the dipole, but the conservation of angular momentum causes more complexity in this interaction, causing it to move in a more complex manner such as precession.

Energy Dissipation

Energy dissipation refers to the process by which a system loses energy over time, usually as heat or thru friction-like effects. For a dipole, once it starts aligning with the magnetic field, if it has no angular momentum, energy can naturally dissipate and allow a perfect alignment.

• Without angular momentum, a dipole can slowly shed energy, becoming progressively more aligned until it rests in this state.
• An oscillating dipole can lose energy via processes similar to friction, slowing down any wobbling or movement.

However, for a dipole with angular momentum, continuous rotation prevents it from reaching full alignment. Instead of stopping, it precesses—a behavior similar to how a spinning top wobbles. As a result, the energy dissipation isn't enough to stop its motion entirely unless external forces are applied to counteract the rotating momentum.