Educational

Introduction to Magnetism

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by

Saim Khalid
in

Magnetism is the force exerted by magnets when they attract or repel each other or other materials. Historically, lodestones were the first naturally occurring magnets discovered thousands of years ago. William Gilbert, in the 16th century, studied magnetism systematically and recognized Earth as a giant magnet.

Types of Magnets

  1. Natural Magnets: Lodestones and magnetite
  2. Artificial Permanent Magnets: Bar magnets, horseshoe magnets
  3. Electromagnets: Created by electric current through a coil

Magnetic Poles

  • Every magnet has north (N) and south (S) poles.
  • Like poles repel, unlike poles attract.
  • Poles cannot exist independently; cutting a magnet always produces two smaller magnets, each with N and S poles.

2. Magnetic Fields and Lines of Force

A magnetic field is the region around a magnet where magnetic forces can be observed. Magnetic fields are vector quantities, having both magnitude and direction.

Magnetic Lines of Force

  • Emanate from the north pole and enter the south pole
  • Never intersect
  • The density of lines indicates field strength

Visualizing Magnetic Fields

  • Iron filings: Arrange along field lines
  • Compasses: Needle aligns along the tangent to the magnetic field

3. Earth’s Magnetism

Earth behaves like a giant bar magnet:

  • Magnetic poles are different from geographic poles
  • Magnetic declination: Angle between geographic north and magnetic north
  • Magnetic inclination: Angle made by the field with the horizontal
  • Earth’s magnetic field enables navigation using compasses

4. Magnetic Force on Moving Charges

When a charged particle moves through a magnetic field, it experiences a Lorentz force: F⃗=q(v⃗×B⃗)\vec{F} = q (\vec{v} \times \vec{B})F=q(v×B)

Where:

  • qqq = charge
  • v⃗\vec{v}v = velocity of the particle
  • B⃗\vec{B}B = magnetic field

Applications

  • Cathode ray tubes (CRTs)
  • Cyclotrons and particle accelerators

Charged particles move in circular or helical paths depending on the velocity direction relative to the field.

5. Magnetic Force on Current-Carrying Conductors

Current-carrying conductors in a magnetic field experience a force: F⃗=I(L⃗×B⃗)\vec{F} = I (\vec{L} \times \vec{B})F=I(L×B)

Where:

  • III = current
  • LLL = length vector of the conductor

Fleming’s Left-Hand Rule: Determines direction of force on a conductor.

Applications:

  • Electric motors
  • Galvanometers

6. Torque on a Current Loop

A current-carrying loop in a uniform magnetic field experiences a torque: τ=nIABsin⁡θ\tau = n I A B \sin \thetaτ=nIABsinθ

Where:

  • nnn = number of turns
  • III = current
  • AAA = area of the loop
  • θ\thetaθ = angle between field and normal

Applications:

  • Galvanometers
  • Electric motors

7. Biot-Savart Law

The Biot-Savart Law allows calculation of the magnetic field due to a small current element: dB⃗=μ04πIdl⃗×r^r2d\vec{B} = \frac{\mu_0}{4\pi} \frac{I d\vec{l} \times \hat{r}}{r^2}dB=4πμ0​​r2Idl×r^​

Where:

  • μ0\mu_0μ0​ = permeability of free space
  • dl⃗d\vec{l}dl = element of the conductor
  • rrr = distance from the element

Applications include field of a circular loop, solenoid, and straight conductor.

8. Ampere’s Circuital Law

Ampere’s law relates the integral of the magnetic field along a closed loop to the current enclosed: ∮B⃗⋅dl⃗=μ0Ienclosed\oint \vec{B} \cdot d\vec{l} = \mu_0 I_{enclosed}∮B⋅dl=μ0​Ienclosed​

Applications:

  • Solenoids: B=μ0nIB = \mu_0 n IB=μ0​nI
  • Toroids: Uniform field inside the core

9. Electromagnets

An electromagnet is created by passing current through a coil around a soft iron core:

  • Strength depends on current, number of turns, and core material
  • Soft iron core enhances field
  • Reversible by switching current direction

Applications:

  • Cranes for lifting heavy metals
  • Relays and switches
  • MRI machines

10. Magnetic Properties of Materials

Materials respond differently to magnetic fields:

  1. Diamagnetic: Weakly repelled (e.g., bismuth)
  2. Paramagnetic: Weakly attracted (e.g., aluminum)
  3. Ferromagnetic: Strongly attracted, exhibit hysteresis (e.g., iron, cobalt, nickel)

Hysteresis: Lag between magnetization and applied field, important in transformers and magnetic storage.

11. Faraday’s Law of Electromagnetic Induction

Faraday’s Law: Changing magnetic flux through a coil induces an emf: E=−dΦBdt\mathcal{E} = – \frac{d\Phi_B}{dt}E=−dtdΦB​​

Where:

  • ΦB=B⋅A⋅cos⁡θ\Phi_B = B \cdot A \cdot \cos\thetaΦB​=B⋅A⋅cosθ = magnetic flux

Lenz’s Law: The induced emf opposes the change in flux.

Applications:

  • Generators
  • Induction cookers
  • Electric guitars (pickups)

12. Self-Inductance and Mutual Inductance

12.1 Self-Inductance

  • Coil opposes change in its own current
  • Induced emf: E=−LdIdt\mathcal{E} = -L \frac{dI}{dt}E=−LdtdI​

12.2 Mutual Inductance

  • Changing current in one coil induces emf in nearby coil:

E2=−MdI1dt\mathcal{E}_2 = -M \frac{dI_1}{dt}E2​=−MdtdI1​​

Applications:

  • Transformers
  • Inductive sensors

13. Alternating Currents and Inductance

AC current induces varying magnetic flux, producing inductive reactance: XL=2πfLX_L = 2 \pi f LXL​=2πfL

Where:

  • fff = frequency
  • LLL = inductance

Voltage and current can be out of phase, requiring phasor analysis.

14. Transformers

Transformers operate on mutual induction: VsVp=NsNp\frac{V_s}{V_p} = \frac{N_s}{N_p}Vp​Vs​​=Np​Ns​​

Where:

  • Vs,VpV_s, V_pVs​,Vp​ = secondary and primary voltages
  • Ns,NpN_s, N_pNs​,Np​ = number of turns

Step-up and step-down transformers conserve energy: Pprimary=Psecondary(ignoring losses)P_{primary} = P_{secondary} \quad (\text{ignoring losses})Pprimary​=Psecondary​(ignoring losses)

Applications:

  • Power distribution
  • Electronics chargers
  • High-voltage transmission

15. Electromagnetic Waves

Maxwell’s equations unify electricity and magnetism:

  • Changing electric field produces magnetic field and vice versa
  • Propagates as electromagnetic waves at speed of light (c ≈ 3 × 10^8 m/s)
  • Frequency and wavelength determine type: radio, microwave, visible, X-ray

Applications:

  • Communication systems
  • Wi-Fi, radio, television

16. Applications of Electromagnetism

  1. Motors and Generators: Convert between mechanical and electrical energy
  2. Induction Heating: Cookers and industrial heating
  3. Magnetic Levitation: Trains and frictionless systems
  4. Wireless Power Transfer: Charging electric devices
  5. Medical Imaging: MRI machines rely on strong magnetic fields

17. Practical Experiments

17.1 Magnetic Field Visualization

  • Iron filings around a bar magnet
  • Compass needle alignment

17.2 Electromagnetic Induction

  • Move a magnet through a coil
  • Observe induced current on a galvanometer

17.3 Solenoid Experiment

  • Vary current and number of turns
  • Measure magnetic field with a teslameter

18. Problem Solving in Magnetism and Electromagnetism

  1. Determine magnetic field due to straight conductor: B=μ0I2πrB = \frac{\mu_0 I}{2 \pi r}B=2πrμ0​I​
  2. Force on conductor: F=ILBsin⁡θF = I L B \sin \thetaF=ILBsinθ
  3. Induced emf in coil: E=−NdΦdt\mathcal{E} = -N \frac{d\Phi}{dt}E=−NdtdΦ​
  4. Transformers: Use voltage ratio to find turns required

Sample Problem:

Problem: A 10-turn coil rotates in a 0.5 T magnetic field at 60 rev/min. Coil area 0.02 m². Find induced emf.

Solution: f=6060=1 Hz,Φ=BA=0.5×0.02=0.01 Wbf = \frac{60}{60} = 1\, \text{Hz}, \quad \Phi = B A = 0.5 \times 0.02 = 0.01\, \text{Wb}f=6060​=1Hz,Φ=BA=0.5×0.02=0.01Wb Emax=N⋅2πf⋅Φ=10⋅2π⋅1⋅0.01≈0.628 V\mathcal{E}_{max} = N \cdot 2\pi f \cdot \Phi = 10 \cdot 2\pi \cdot 1 \cdot 0.01 \approx 0.628\, VEmax​=N⋅2πf⋅Φ=10⋅2π⋅1⋅0.01≈0.628V

19. Safety Considerations

  • High currents can produce strong magnetic fields, causing hazards
  • Transformers and inductive devices should be insulated
  • MRI machines require careful handling of ferromagnetic objects

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