Magnetic Dipoles and Interactions

Discusses magnetic fields generated by electric currents.
Contrast with intrinsic magnetization of objects like bar magnets.
Magnetic fields arise due to electron "spin"; charges moving at the microscopic level.

A magnetic dipole has a moment that points from the south to the north pole of a bar magnet.
When placed in an external magnetic field, dipoles experience torque, represented mathematically as:
- ( \tau = \mu \times B )
- Torque (( \tau )) is a vector force acting on the dipole.
Potential energy (PE) in a magnetic field is given by:
- ( PE = -\mu \cdot B )
- PE is minimized when aligned with the field (( \theta = 0 )).
- Maximum when perpendicular (( \theta = 90^\circ )).

Bar magnets are essentially small dipoles with distinct north and south poles (unlike electric charges which can exist independently).
If a bar magnet is broken, it forms two smaller magnets, each with its own north and south pole (no magnetic monopoles).

Current loops also create magnetic dipoles, characterized by:
- ( \mu = I \cdot A ) (I = current; A = area of the loop).
A compass needle behaves as a dipole, aligning with external magnetic fields.
Earth behaves like a giant bar magnet with magnetic poles misplaced from the geographic poles.

Magnetic field lines illustrate the direction of a magnetic field:
- Lines are denser where the field is stronger.
- They never cross and always form closed loops.
Understanding field lines helps in predicting the behavior of magnetic materials and the forces exerted by fields.

Diamagnetic
- Have no unpaired electron spins; cause weak repulsion in magnetic fields.
- Induced field is in the opposite direction of the external field.
- Examples: Water, most substances.
Paramagnetic
- Have unpaired electron spins that result in a net magnetic dipole; weakly attracted to magnetic fields.
- Induced field is in the same direction as the external field.
- Becomes more magnetic at lower temperatures due to reduced thermal agitation.
Ferromagnetic
- Strongly attracted to magnetic fields; can retain permanent magnetization.
- Exhibit magnetic domains that can align under an external field.
- Common materials include iron and cobalt.

Induced Magnetization:
- When placed in a magnetic field, materials exhibit induced magnetization characterized by magnetic susceptibility (( \chi )).
- The resultant magnetic field inside the material can be modeled using:
- ( B = B{ext} + B{induced} = (1 + \chi) B_{ext} )
The types of responses to external fields are categorized based on the susceptibility value:
- ( \chi < 0 ) for diamagnets (weak repelling).
- ( \chi > 0 ) for paramagnets (weak attracting).

Electron spins are the foundation of magnetic dipoles in materials:
- Orbital angular momentum and intrinsic spin contribute to magnetic moments.
- Pauli exclusion principle leads to paired spins canceling out each other's dipole moment in diamagnets and some paramagnets.

In the absence of an external magnetic field, ferromagnetic materials have domains with aligned spins.
When exposed to a magnetic field, these domains can grow and align further, leading to a combined, strong magnetic field.
Hysteresis is a characteristic of ferromagnetic materials, which can retain magnetization after the field is removed.

Electromagnets are produced using electric currents in coiled wire (solenoids).
Adding ferromagnetic materials enhances the magnetic field produced by the current.
Superconducting electromagnets can produce extremely high magnetic fields (up to 40 T).

Magnetic moments are found in materials based on electron configurations and behaviors.
Magnetic dipoles interact differently based on material classification: diamagnetic, paramagnetic, or ferromagnetic.
Understanding these concepts is crucial for technology involving magnets and electromagnetic devices.