Magnetism and Matter

What is the defining equation for the magnetic field, B, in terms of the force on a moving charge?

The magnetic field B is defined by the equation for the magnetic force on a charge q moving with velocity v: $F = q(v \times B)$.

What is a key distinction between magnetic field lines (B) and electric field lines (E) regarding their structure?

Magnetic field lines form continuous closed loops because there are no magnetic monopoles, whereas electric field lines start on positive charges and end on negative charges.

What does the pattern of iron filings around a bar magnet suggest about its nature?

The pattern suggests that the bar magnet acts as a magnetic dipole, with two distinct poles.

What is the orientation of the magnetic field due to a short bar magnet at a point on its axial line (end-on position)?

The magnetic field is along the axis of the magnet, given by the formula $BA = \frac{\mu0}{4\pi} \frac{2m}{r^3}$ for $r \gg l$.

What is the orientation of the magnetic field due to a short bar magnet at a point on its equatorial line (broadside-on position)?

The magnetic field is parallel to the axis but in the opposite direction of the magnetic moment, given by $BE = -\frac{\mu0}{4\pi} \frac{m}{r^3}$ for $r \gg l$.

How is magnetic flux, $\phi$, defined for a uniform magnetic field B passing through a flat area A?

Magnetic flux is defined as the scalar product of the magnetic field and the area vector: $\phi = B \cdot A = BA \cos{\theta}$.

What is the formula for magnetic flux, $\phi$, for a non-uniform magnetic field B over a surface?

For a non-uniform field, the magnetic flux is the surface integral of the magnetic field over the area: $\phi = \int B \cdot dA$.

What is the SI unit of magnetic flux?

The SI unit of magnetic flux is the weber (Wb).

What is the SI unit of magnetic field strength (B)?

The SI unit for magnetic field strength is the tesla (T).

Term: Diamagnetic substances

Substances that, when placed in a magnetic field, acquire a feeble magnetism opposite to the direction of the field and are weakly repelled.

Term: Paramagnetic substances

Substances that, when placed in a magnetic field, acquire a feeble magnetism in the direction of the field and are weakly attracted.

Term: Ferromagnetic substances

Substances that, when placed in a magnetic field, become strongly magnetized in the direction of the field and are strongly attracted.

What is the fundamental cause of magnetization (M) in materials?

Magnetization is caused by the net magnetic dipole moment (m) of the atoms, ions, or molecules within the material.

How does the atomic magnetic dipole moment differ among diamagnetic, paramagnetic, and ferromagnetic materials?

The net atomic magnetic dipole moment is zero for diamagnetic, small but greater than zero for paramagnetic, and large and greater than zero for ferromagnetic materials.

In which direction is the induced magnetization in a diamagnetic substance relative to the external magnetic field B?

A very small magnetization is induced in the direction opposite to the external magnetic field.

How do ferromagnetic materials behave when placed in an external magnetic field B?

They develop a large magnetization parallel to the external magnetic field B.

How do the magnetic field lines change when passing through a diamagnetic material?

The magnetic field lines become less dense, indicating a weakened field inside the material.

How do the magnetic field lines change when passing through a paramagnetic material?

The magnetic field lines become slightly more dense, indicating a slightly enhanced field inside the material.

How do the magnetic field lines change when passing through a ferromagnetic material?

The magnetic field lines become much more dense, indicating a strongly enhanced field inside the material.

How does a small bar of diamagnetic material align itself when suspended in a uniform horizontal magnetic field?

It aligns itself perpendicular to the direction of the magnetic field.

How does a small bar of paramagnetic or ferromagnetic material align itself when suspended in a uniform horizontal magnetic field?

It aligns itself parallel to the direction of the magnetic field.

What is the defining equation for magnetic intensity, H?

Magnetic intensity H is defined by the equation $H = (B/\mu_0) - M$.

Term: Magnetic Susceptibility ($\chi_m$)

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

What is the sign of magnetic susceptibility ($\chi_m$) for a diamagnetic substance?

The magnetic susceptibility is small and negative ($\chi_m < 0$) for diamagnetic substances.

What is the sign of magnetic susceptibility ($\chi_m$) for a paramagnetic substance?

The magnetic susceptibility is small and positive ($\chi_m > 0$) for paramagnetic substances.

What is the characteristic value of magnetic susceptibility ($\chi_m$) for a ferromagnetic substance?

The magnetic susceptibility is large and positive ($\chi_m \gg 1$) for ferromagnetic substances.

What is the relationship between relative magnetic permeability ($\mur$) and magnetic susceptibility ($\chim$)?

The relative magnetic permeability is related to susceptibility by the equation $\mur = 1 + \chim$.

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

For diamagnetic materials, the relative permeability is less than 1 ($0 \le \mu_r < 1$).

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

For paramagnetic materials, the relative permeability is slightly greater than 1 ($\mu_r > 1$).

What is the typical range for the relative permeability ($\mu_r$) of ferromagnetic materials?

For ferromagnetic materials, the relative permeability is very large ($\mu_r \gg 1$).

What is Curie's Law for paramagnetic substances?

Curie's Law states that the magnetic susceptibility ($\chim$) of a paramagnetic substance is inversely proportional to the absolute temperature (T), or $\chim \propto 1/T$.

How does the magnetic susceptibility of a diamagnetic substance depend on temperature?

The magnetic susceptibility of a diamagnetic substance is independent of temperature.

Term: Curie Temperature

The critical temperature above which a ferromagnetic material loses its ferromagnetic properties and behaves like a paramagnetic material.

What is an electromagnet?

A type of magnet in which the magnetic field is produced by an electric current, typically made of a soft iron core inside a coil of wire.

The lagging of magnetic induction (B) behind the magnetizing field (H) in a ferromagnetic material is known as _.

hysteresis

Term: Retentivity

The ability of a magnetic material to retain its magnetism after the external magnetizing field is removed.

Term: Coercivity

The measure of a magnetic material's ability to resist demagnetization by an external magnetic field, or the reverse field needed to reduce its magnetization to zero.

What magnetic properties are desirable for a material used to make a permanent magnet?

A material for a permanent magnet should have high retentivity and high coercivity.

What magnetic properties are desirable for the core of an electromagnet or transformer?

The core material should have high permeability, low retentivity, low coercivity, and low hysteresis loss.

Why is soft iron a suitable material for making electromagnets?

Soft iron is suitable because it has high permeability, low retentivity, and a small area of hysteresis loop, which means low energy loss.

Why is steel a suitable material for making permanent magnets?

Steel is suitable because it has high retentivity and high coercivity, allowing it to remain magnetized.

The fact that magnetic field lines form closed loops is a consequence of _ Law for magnetism.

Gauss's

What is the mathematical statement of Gauss's Law for magnetism?

The net magnetic flux through any closed surface is zero: $\sum B \cdot \Delta S = 0$.

What fundamental aspect of magnetism does Gauss's law reflect?

It reflects the fact that isolated magnetic poles (monopoles) are not known to exist.

What happens to the field lines and the field strength inside a diamagnetic material placed in an external magnetic field?

The field lines are expelled, and the magnetic field inside the material is reduced.

In a non-uniform magnetic field, a diamagnetic substance tends to move from a region of field to a region of field.

stronger; weaker

In a non-uniform magnetic field, a paramagnetic substance tends to move from a region of field to a region of field.

weak; strong

In ferromagnetic materials, atoms spontaneously align themselves in macroscopic volumes called _.

domains

What is the relationship between the total magnetic field B, magnetic intensity H, and magnetization M?

$B = \mu_0 (H + M)$

A current-carrying loop behaves as a _, with its moment given by M = IA.

magnetic dipole