6.1 Magnetism and Electromagnetism

Magnetism and Electromagnetism in Aviation

In the realm of aircraft maintenance engineering, a profound understanding of magnetism and electromagnetism is not merely theoretical; it is a fundamental requirement for ensuring the airworthiness and safety of complex electrical systems. From the engine-driven magnetos that provide independent ignition spark to reciprocating engines, to the heavy-duty starter-generators that start turbine engines and power DC buses, magnetic fields are the primary mechanism for energy conversion. Relays, solenoids, control valves, transformers, and analog flight instruments all rely on the interactions of magnetic fields. Furthermore, as modern aircraft rely heavily on sensitive microelectronics, technicians must understand magnetic shielding, permeability, and electromagnetic interference (EMI) to isolate and protect critical flight guidance and communication systems.

The Nature and Theory of Magnetism

At the subatomic level, magnetism arises from the orbital motion and spin of electrons. Every electron behaves as a microscopic magnetic dipole. In most materials, these dipoles are randomly oriented, canceling each other out. However, in certain materials known as ferromagnetic materials (such as iron, cobalt, and nickel), quantum mechanical effects cause adjacent dipoles to align in parallel regions called magnetic domains (or Weiss domains).

When an unmagnetized piece of ferromagnetic material is placed in an external magnetic field, two things happen: domains aligned with the external field grow at the expense of non-aligned domains, and the orientation of other domains rotates toward the external field. If the external field is strong enough, all domains align completely. At this point, the material is said to have reached magnetic saturation, meaning that further increases in the magnetizing force will not increase the material's magnetic strength.

Classifications of Magnetic Materials

• Ferromagnetic: Materials with extremely high magnetic susceptibility that are strongly attracted to magnetic fields (e.g., iron, soft steel, Permalloy). Their relative permeability ($\mu_r$) is very large (hundreds to thousands).
• Paramagnetic: Materials that are weakly attracted by magnetic fields (e.g., aluminum, platinum, oxygen). Their relative permeability is slightly greater than 1.
• Diamagnetic: Materials that are weakly repelled by magnetic fields (e.g., copper, gold, bismuth, water). Their relative permeability is slightly less than 1.

Magnetic Fields and Lines of Force

A magnetic field is the region around a magnet where magnetic forces can be detected. This field is represented by imaginary magnetic lines of force (or magnetic flux lines). These lines possess specific physical properties that are heavily tested on EASA exams:

1. They exit the North pole and enter the South pole externally, completing their loop internally from South to North.
2. They form continuous, closed loops.
3. They never cross or intersect one another.
4. They behave like stretched elastic bands, seeking to contract to the shortest possible path.
5. They repel each other laterally when flowing in the same direction.

Magnetic Circuit Parameters and Ohm's Law for Magnetic Circuits

To design and analyze electromagnets, transformers, and motor cores, engineers and technicians use a framework analogous to electric circuits. The table below outlines the direct relationships between electrical and magnetic parameters:

Defining the Formulas

• Magnetomotive Force (MMF, $\mathcal{F}$): The driving force behind magnetic flux. It is proportional to the number of turns in a coil ($N$) and the current flowing through it ($I$): $\mathcal{F} = N \cdot I$
• Magnetic Flux ($\Phi$): The total number of magnetic lines of force. One Weber ($Wb$) equals $10^8$ lines of force (maxwells).
• Reluctance ($\mathcal{R}$): The opposition a material offers to the passage of magnetic flux. Unlike electrical resistance, reluctance does not dissipate energy as heat. It depends on the physical dimensions and permeability of the material: $\mathcal{R} = \frac{l}{\mu \cdot A}$ Where $l$ is the mean length of the magnetic path (meters), $A$ is the cross-sectional area ($m^2$), and $\mu$ is the absolute permeability.
• Permeability ($\mu$): The ease with which a material permits magnetic flux. It is calculated as: $\mu = \mu_0 \cdot \mu_r$ Where $\mu_0 = 4\pi \times 10^{-7}\text{ H/m}$ is the permeability of free space (vacuum), and $\mu_r$ is the relative permeability of the material (dimensionless).
• Ohm's Law for Magnetic Circuits (Hopkinson's Law): $\mathcal{F} = \Phi \cdot \mathcal{R}$
• Flux Density ($B$): The concentration of magnetic flux per unit area, measured in Teslas ($T$) or Webers per square meter ($Wb/m^2$): $B = \frac{\Phi}{A}$
• Magnetic Field Strength ($H$, Magnetizing Force): The MMF applied per unit length of the magnetic path: $H = \frac{\mathcal{F}}{l} = \frac{N \cdot I}{l}$ This allows us to relate flux density to field strength via: $B = \mu \cdot H$.

The Hysteresis Loop (B-H Curve)

When a ferromagnetic material is subjected to a changing magnetic field strength ($H$), the resulting flux density ($B$) does not change in direct proportion. Instead, the change in $B$ lags behind the change in $H$. This phenomenon is called hysteresis (derived from the Greek word meaning 'lagging behind'). A plot of $B$ against $H$ over a complete cycle of magnetization forms a hysteresis loop.

• Magnetization Path: Starting with an unmagnetized core ($B=0, H=0$), as $H$ increases, $B$ rises along the initial magnetization curve until reaching saturation.
• Remanence ($B_r$, Residual Magnetism): When $H$ is reduced back to zero, some magnetic flux remains in the core. The value of $B$ at $H = 0$ is the remanence. Residual magnetism is critical for DC generators because it provides the initial magnetic field required to start the generation process (self-excitation) when the engine starts.
• Coercivity ($H_c$, Coercive Force): To reduce the residual flux density to zero, a reverse magnetizing force must be applied. The value of $-H$ required to make $B = 0$ is the coercivity.
• Hysteresis Loss: The area enclosed by the hysteresis loop represents energy lost as heat due to the friction of magnetic domains rotating back and forth. For AC applications (like transformers and AC generator stators), materials with a narrow hysteresis loop (e.g., silicon steel, soft iron) are chosen to minimize this heat loss. For permanent magnets, materials with wide loops, high remanence, and high coercivity (e.g., Alnico, NdFeB) are required.

Electromagnetism and Right-Hand Rules

Electromagnetism is the production of a magnetic field by the flow of electric current. In 1820, Hans Christian Oersted discovered that a magnetic compass needle is deflected when placed near a current-carrying wire.

Right-Hand Grip Rule for a Straight Conductor

To determine the direction of the magnetic field around a straight wire carrying conventional current (flowing from positive to negative):

1. Grasp the conductor with your right hand.
2. Point your thumb in the direction of the conventional current flow.
3. Your curled fingers point in the direction of the magnetic field lines (concentric circles around the wire).

If current is flowing away from you (represented by a cross $\otimes$, like the feathers of an arrow), the field is clockwise. If current is flowing toward you (represented by a dot $\odot$, like the tip of an arrow), the field is counter-clockwise.

Right-Hand Rule for a Solenoid (Coil)

When a wire is wound into a coil (solenoid), the magnetic fields around individual turns combine to form a stronger, unified magnetic field similar to that of a bar magnet. To identify the poles of an electromagnet:

1. Grasp the coil with your right hand.
2. Curl your fingers in the direction of the conventional current flowing through the loops.
3. Your extended thumb points in the direction of the magnetic North pole of the coil.

Worked Exam Calculation Scenario

Problem: An aircraft relay core consists of a soft iron ring with a mean circumference (length) of $0.4\text{ meters}$ and a cross-sectional area of $1.5 \times 10^{-4}\text{ m}^2$. The relative permeability of the soft iron core is $2000$. A coil of $500\text{ turns}$ is wound around the core. Calculate the current required to establish a magnetic flux of $3.0 \times 10^{-4}\text{ Webers}$ in the core.

Step 1: Calculate the absolute permeability ($\mu$) of the core. $\mu = \mu_0 \cdot \mu_r = (4\pi \times 10^{-7}\text{ H/m}) \times 2000 \approx 2.513 \times 10^{-3}\text{ H/m}$

Step 2: Calculate the reluctance ($\mathcal{R}$) of the magnetic circuit. $\mathcal{R} = \frac{l}{\mu \cdot A} = \frac{0.4}{2.513 \times 10^{-3} \times 1.5 \times 10^{-4}} = \frac{0.4}{3.77 \times 10^{-7}} \approx 1.061 \times 10^6\text{ At/Wb}$

Step 3: Calculate the required Magnetomotive Force (MMF, $\mathcal{F}$). $\mathcal{F} = \Phi \cdot \mathcal{R} = (3.0 \times 10^{-4}\text{ Wb}) \times (1.061 \times 10^6\text{ At/Wb}) \approx 318.3\text{ Ampere-turns}$

Step 4: Calculate the required current ($I$). $\mathcal{F} = N \cdot I \implies I = \frac{\mathcal{F}}{N} = \frac{318.3}{500} \approx 0.637\text{ Amperes}$

Answer: A current of approximately $0.64\text{ A}$ (or $637\text{ mA}$) must flow through the coil to generate the required magnetic flux.

Exam Traps and Tips

• Conventional vs. Electron Flow: Always ensure you are applying the right-hand rule with conventional current (positive to negative). If an EASA question specifies electron flow (negative to positive), you must either reverse the result of your right-hand rule or use your left hand.
• Reluctance does not dissipate heat: A common trap is assuming reluctance is identical to resistance. While they are mathematically analogous, reluctance does not lead to $I^2 R$ heat dissipation. Hysteresis and eddy currents are the sources of heat loss in magnetic circuits.
• Relative Permeability is Unitless: Remember that $\mu_r$ has no unit, but absolute permeability $\mu$ is measured in Henries per meter ($H/m$).