Unit 2: Electromagnetism (PHYDSM252T)
Table of Contents
1. Biot-Savart's Law and Applications
Biot-Savart's Law describes the magnetic field produced by a steady electric current. It relates the magnetic field dB to the magnitude, direction, length, and proximity of the electric current.
Applications:
- Straight Conductor: Calculating the magnetic field at a point near a long straight wire carrying current.
- Circular Coil: Finding the magnetic field at the center or on the axis of a current-carrying circular loop.
- Solenoid: Determining the uniform magnetic field inside a long current-carrying solenoid.
2. Divergence and Curl of Magnetic Field
The behavior of magnetic fields is mathematically described by their divergence and curl:
- Divergence (∇·B): The divergence of a magnetic field is always zero, indicating that there are no magnetic monopoles.
- Curl (∇×B): The curl of a magnetic field is related to the current density, which forms the basis for Ampere's law.
3. Magnetic Vector Potential
The Magnetic Vector Potential (A) is a vector field whose curl is equal to the magnetic field B (B = ∇×A). It is a useful tool in solving complex electromagnetic problems where the field B might be difficult to calculate directly.
4. Ampere's Circuital Law and Applications
Ampere's Circuital Law states that the line integral of the magnetic field B around a closed loop is equal to μ₀ times the total current passing through the loop.
Applications:
- Solenoid: Used to derive the magnetic field B = μ₀ni inside an ideal solenoid.
- Toroidal Coils: Calculating the magnetic field inside the core of a toroid.
5. Magnetic Properties of Materials
When materials are placed in a magnetic field, they respond based on their internal structure. Key terms include:
- Magnetic Intensity (H): The external field applied to a material.
- Magnetic Induction (B): The total magnetic field within the material.
- Permeability (μ): The ability of a material to allow magnetic flux to pass through it.
- Magnetic Susceptibility (χ): A measure of how much a material will become magnetized in an applied magnetic field.
6. Classification of Magnetic Materials
Materials are classified into three main categories based on their magnetic behavior:
| Type | Description | Susceptibility (χ) |
|---|---|---|
| Diamagnetic | Feebly repelled by a magnetic field; atoms have no permanent dipole moment. | Small and Negative |
| Paramagnetic | Feebly attracted by a magnetic field; atoms have permanent dipole moments that align with the field. | Small and Positive |
| Ferromagnetic | Strongly attracted by a magnetic field; possess domains that align even with weak fields. | Large and Positive |
Exam Focus Corner
Frequently Asked Questions
- Derive the expression for the magnetic field of a long straight conductor using Ampere's law.
- Distinguish between Diamagnetic and Paramagnetic materials based on their susceptibility.
Common Mistakes
- Current Direction: Always use the Right-Hand Thumb Rule to determine the direction of the magnetic field B relative to current I.
- B vs H: Confusing Magnetic Induction (B) with Magnetic Intensity (H). Remember: B = μH.
Quick Mnemonics
Biot-Savart: "Big Small Law" (B is related to Current I and distance r²).