Magnetism and Matter

How is a current-carrying loop conceptually treated in magnetism?

It is treated as a magnetic dipole.

What is the formula for the magnetic dipole moment, $m$, of a current loop with $N$ turns, area $A$, and current $I$?

The formula is $m = NIA$.

What gives rise to the magnetic dipole moment of a revolving electron?

The orbital motion of the electron, which is equivalent to a tiny current loop, creates a magnetic dipole moment.

In a uniform magnetic field $B$, what is the net force experienced by a magnetic dipole?

The net force on a magnetic dipole in a uniform magnetic field is zero.

What is the vector expression for the torque ($\tau$) experienced by a magnetic dipole with moment $m$ in a uniform magnetic field $B$?

The torque is given by the cross product $\tau = m \times B$.

What is the magnitude of the torque on a magnetic dipole when its magnetic moment $m$ makes an angle $\theta$ with a uniform magnetic field $B$?

The magnitude of the torque is $\tau = mB \sin{\theta}$.

Qualitatively, in which direction does the magnetic field point on the axial line of a bar magnet (magnetic dipole)?

The magnetic field on the axial line points along the direction of the magnetic moment, from the south pole to the north pole.

Qualitatively, in which direction does the magnetic field point on the equatorial line of a bar magnet (magnetic dipole)?

The magnetic field on the equatorial line points in the direction opposite to the magnetic moment.

Why is a bar magnet considered an equivalent solenoid?

A bar magnet is considered an equivalent solenoid because the magnetic field lines for both are very similar, especially at large distances.

Substances that are weakly repelled by a magnetic field and tend to move from stronger to weaker parts of the field are called _ substances.

diamagnetic

What is the characteristic of the magnetic susceptibility ($\chi$) for diamagnetic materials?

The magnetic susceptibility ($\chi$) for diamagnetic materials is small and negative.

What is the characteristic of the relative permeability ($\mu_r$) for diamagnetic materials?

The relative permeability ($\mu_r$) for diamagnetic materials is slightly less than 1.

What is the origin of diamagnetism?

Diamagnetism arises from an induced magnetic moment in atoms that is opposite to the direction of the external magnetic field.

Substances that are weakly attracted by a magnetic field and tend to move from weaker to stronger parts of the field are called _ substances.

paramagnetic

What is the characteristic of the magnetic susceptibility ($\chi$) for paramagnetic materials?

The magnetic susceptibility ($\chi$) for paramagnetic materials is small and positive.

What is the characteristic of the relative permeability ($\mu_r$) for paramagnetic materials?

The relative permeability ($\mu_r$) for paramagnetic materials is slightly greater than 1.

What is the origin of paramagnetism?

Paramagnetism arises from the presence of permanent atomic magnetic moments that tend to align with an external magnetic field.

What law describes the relationship between magnetic susceptibility and absolute temperature for paramagnetic materials?

Curie's Law, which states that susceptibility is inversely proportional to the absolute temperature ($\chi \propto 1/T$).

Substances that are strongly attracted by a magnetic field are called _ substances.

ferromagnetic

What is the characteristic of the magnetic susceptibility ($\chi$) and relative permeability ($\mu_r$) for ferromagnetic materials?

For ferromagnetic materials, both susceptibility ($\chi$) and relative permeability ($\mur$) are very large and positive ($\mur \gg 1$).

What is the origin of the strong magnetic effects in ferromagnetic materials?

It is due to the spontaneous alignment of atomic magnetic moments into macroscopic regions called domains.

What is the Curie temperature?

The Curie temperature is the temperature above which a ferromagnetic material loses its ferromagnetic properties and behaves like a paramagnetic material.

What type of material is used to make electromagnets?

Soft ferromagnetic materials, such as soft iron, are used to make electromagnets.

What are two key properties of the material chosen for an electromagnet's core?

The material should have high permeability and low retentivity.

What type of material is used to make permanent magnets?

Hard ferromagnetic materials, such as steel or Alnico, are used to make permanent magnets.

What are two key properties of the material chosen for a permanent magnet?

The material should have high retentivity and high coercivity.

Term: Magnetic potential energy ($U_m$)

Definition: The energy stored in a magnetic dipole when placed in an external magnetic field, given by the formula $U_m = -m \cdot B$.

At what orientation is the potential energy of a magnetic dipole in a uniform magnetic field at its minimum (most stable)?

The potential energy is minimum when the magnetic moment is parallel to the magnetic field ($\theta = 0^\circ$).

At what orientation is the potential energy of a magnetic dipole in a uniform magnetic field at its maximum (most unstable)?

The potential energy is maximum when the magnetic moment is anti-parallel to the magnetic field ($\theta = 180^\circ$).

What is the defining characteristic of magnetic field lines that distinguishes them from electrostatic field lines?

Magnetic field lines always form continuous closed loops because magnetic monopoles do not exist.

What does Gauss's law for magnetism state about the net magnetic flux through any closed surface?

It states that the net magnetic flux through any closed surface is always zero.

What is the mathematical expression for Gauss's law for magnetism?

The expression is $\oint B \cdot dS = 0$.

What fundamental aspect of magnetism is implied by Gauss's law for magnetism?

It implies that isolated magnetic poles (magnetic monopoles) are not known to exist.

Term: Magnetization (M)

Definition: The net magnetic dipole moment per unit volume of a magnetic material.

Term: Magnetic intensity (H)

Definition: A vector field that represents the part of the total magnetic field due to external sources like currents, independent of the material's response.

How is the total magnetic field $B$ inside a material related to magnetic intensity $H$ and magnetization $M$?

The relationship is given by the equation $B = \mu_0 (H + M)$.

Term: Magnetic susceptibility ($\chi_m$)

Definition: A dimensionless quantity that measures how a magnetic material responds to an external field, defined as the ratio of magnetization to magnetic intensity ($\chi_m = M/H$).

How does the value of magnetic susceptibility ($\chi_m$) relate to the classification of magnetic materials?

$\chi_m$ is negative for diamagnetic, small and positive for paramagnetic, and large and positive for ferromagnetic materials.

Term: Relative magnetic permeability ($\mu_r$)

Definition: A dimensionless quantity that is the ratio of the permeability of a medium to the permeability of free space, related to susceptibility by $\mur = 1 + \chim$.

How does the value of relative permeability ($\mu_r$) relate to the classification of magnetic materials?

$\mur < 1$ for diamagnetic, $\mur > 1$ (slightly) for paramagnetic, and $\mu_r \gg 1$ for ferromagnetic materials.

What is the name for the phenomenon where the magnetization of a ferromagnetic material lags behind the magnetizing field?

This phenomenon is called hysteresis.

Term: Retentivity

Definition: The ability of a ferromagnetic material to retain its magnetization even after the external magnetizing field is removed.

Term: Coercivity

Definition: The measure of the magnetizing field, applied in the opposite direction, required to completely demagnetize a ferromagnetic material.