12.8 Magnetic Fields

Electromagnetism is the branch of physics that studies the relationship between electricity and magnetism. A core concept is that moving electric charges create magnetic fields. A magnetic field is a region of space around a magnet, an electric current, or a moving charged particle, where a magnetic force can be detected.

Sources of Magnetic Fields

Magnetic fields are generated by four main sources:

• Permanent Magnets: Materials like a bar magnet create a persistent magnetic field due to the alignment of electron spins within their atoms.
• Current-Carrying Conductors: As discovered by Hans Christian Oersted, any wire with an electric current flowing through it is surrounded by a magnetic field.
• Moving Charged Particles: An individual charged particle, such as an electron, creates a magnetic field when it is in motion.
• Changing Electric Fields: A fluctuating electric field can also induce a magnetic field.

Visualizing Magnetic Fields with Field Lines

A magnetic field is invisible, but its shape and direction can be visualized using magnetic field lines.

• Method: Sprinkling iron filings around a magnet reveals the pattern of the field lines.
• Direction: By convention, magnetic field lines are drawn as arrows that point out of the North pole and into the South pole of a magnet.
• Strength: The density of the field lines (how close they are to each other) represents the strength of the magnetic field. The field is strongest where the lines are most concentrated, which is at the poles of a magnet.

Properties of Magnetic Field Lines

Magnetic field lines possess the following fundamental properties:

1. Closed Loops: Magnetic field lines always form continuous, closed loops. They do not have a starting or ending point. This is a key difference from electric field lines and implies that magnetic monopoles (isolated North or South poles) do not exist.
2. No Intersections: Field lines never cross each other. If two field lines were to intersect, it would indicate that the magnetic field has two different directions at the same point, which is physically impossible.
3. Vector Quantity: A magnetic field is a vector field, meaning it has both a magnitude (strength) and a direction at every point in space. Its Dimensions→ can be derived from the force equation.

Magnetic Field of a Current-Carrying Wire

Hans Christian Oersted's 1820 experiment demonstrated that an electric current creates a magnetic field.

• Field Shape: The magnetic field around a long, straight, current-carrying wire consists of concentric circles centered on the wire.
• Direction (Right-Hand Grip Rule): The direction of these circular field lines can be determined using the right-hand grip rule:

  Imagine gripping the wire with your right hand so that your thumb points in the direction of the current. The direction that your fingers curl around the wire is the direction of the magnetic field.

Force on a Moving Charge

When a charged particle moves through a magnetic field, it experiences a magnetic (Lorentz) force. The force is given by:

$\vec{F}=q(\vec{v}\times \vec{B})$

In scalar form:

$F=|q|vB\sin \theta$

where $q$ is the charge, $v$ is the speed, $B$ is the magnetic flux density, and $\theta$ is the angle between $\vec{v}$ and $\vec{B}$.

Key consequences:

• The force is always perpendicular to both $\vec{v}$ and $\vec{B}$ (cross product).
• When $\theta =0^{\circ }$ or $180^{\circ }$ (velocity parallel to field): $F=0$.
• When $\theta =90^{\circ }$ (velocity perpendicular to field): $F=qvB$ (maximum).
• Because the force is always perpendicular to velocity, it does no work on the particle and does not change its speed — only its direction.
• A charge entering a uniform field perpendicularly follows a circular path, since the magnetic force acts as a centripetal force: $qvB=\frac{m{v}^2}{r}$, giving radius $r=\frac{mv}{qB}$.

Direction of force: Use the right-hand rule — point fingers in the direction of $\vec{v}$, curl toward $\vec{B}$; the thumb points in the direction of $\vec{F}$ for a positive charge. For a negative charge, the force is reversed.

Possible Questions and Answers

Q: Do magnetic field lines have a physical existence?

A: No, magnetic field lines are a visual and conceptual tool. They are an abstract way to represent the invisible magnetic field's strength and direction, but they are not real physical lines in space.

Q: What would happen if magnetic monopoles were discovered?

A: The discovery of a magnetic monopole (an isolated North or South pole) would be a monumental event in physics. It would mean that magnetic field lines could start or end on a single point, just like electric field lines do on charges. This would require a modification of Maxwell's equations, the fundamental laws of electromagnetism.