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Here is a master cheatsheet for the Magnetic Fields (Chapter 20) section of your 9702 Physics syllabus, optimized for Obsidian.

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🧲 Chapter 20: Magnetic Fields - Master Cheatsheet

Overview

This chapter covers the interaction between magnetic fields, electric currents, and moving charges, as well as the phenomenon of electromagnetic induction.

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1. Concept of a Magnetic Field

• Definition: A region of space where a magnetic material (magnetic pole) or a moving charge experiences a force.
• Representing Fields:
  • Magnetic field lines are continuous loops.
  • Direction: North to South (outside the magnet).
  • Density of lines = Magnitude of Flux Density ($B$).
  • 3D Representation:
    • ● (Dot): Out of the page.
    • × (Cross): Into the page.

Magnetic field representation

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2. Force on a Current-Carrying Conductor

• Equation: $F=BIL\sin \theta$
  • $F$ = Magnetic force (N)
  • $B$ = Magnetic flux density (T)
  • $I$ = Current (A)
  • $L$ = Length of conductor within the field (m)
  • $\theta$ = Angle between the current direction and the magnetic field lines.
• Direction (Fleming’s Left-Hand Rule):
  • Thumb: Motion/Force ($F$)
  • First Finger: Field ($B$)
  • Second Finger: Current ($I$) (Conventional: + to -)

Fleming's Left-Hand Rule

Common Pitfalls

• $F,B,$ and $I$ must be mutually perpendicular for $F=BIL$ to hold at maximum.
• If the current is parallel to field lines, $\theta =0^{\circ }$ or $180^{\circ }$, so $\sin \theta =0$, $F=0$.
• Remember: Direction of current for negative charges (electrons) is opposite to their motion.

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3. Magnetic Flux Density ($B$)

• Definition: The force per unit length per unit current on a straight wire placed at right angles to the magnetic field.
  • Unit: Tesla (T).
  • 1 Tesla = 1 Newton per Ampere-metre.

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4. Forces on a Moving Charge

• Equation: $F=BQv\sin \theta$
  • $Q$ = Charge (C)
  • $v$ = Velocity (m/s)
• Circular Motion: When $v$ is perpendicular to $B$, the magnetic force acts as a centripetal force:
  • $BQv=\frac{m{v}^2}{r}$
  • Radius of path $r=\frac{mv}{BQ}$
• Velocity Selector: Used to filter particles with a specific velocity.
  • Electric force ($F_E=EQ$) equals Magnetic force ($F_B=BQv$).
  • $EQ=BQv⟹v=\frac{E}{B}$

Moving charges

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5. Hall Effect

• Concept: When a conductor carries current in a magnetic field, charges are pushed to one side, creating a potential difference (Hall Voltage, $V_H$).
• Equation: $V_H=\frac{BI}{ntq}$
  • $n$ = number density of charge carriers ($m^{-3}$)
  • $t$ = thickness of the slice
  • $q$ = charge of carrier
• Application: Used to measure magnetic flux density $B$ using a Hall probe.

Hall Probe Tip

Smaller $n$ (semiconductors) gives a larger $V_H$, making them better for sensitive measurements than metals like copper.

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6. Electromagnetic Induction

Magnetic Flux ($\Phi$)

• Definition: Product of magnetic flux density and the cross-sectional area perpendicular to the field.
• Formula: $\Phi =BA\cos \theta$
  • $\theta$ is the angle between the field lines and the normal to the plane of the area.

Magnetic Flux Linkage

• Formula: $N\Phi =BAN\cos \theta$ (for $N$ turns)

Faraday’s & Lenz’s Laws

• Faraday’s Law: The magnitude of induced e.m.f. is proportional to the rate of change of magnetic flux linkage.
  • $\epsilon =N\frac{\Delta \Phi }{\Delta t}$
• Lenz’s Law: The direction of induced e.m.f. is such that it opposes the change in magnetic flux that caused it.
  • $\epsilon =-N\frac{\Delta \Phi }{\Delta t}$ (The negative sign represents Lenz’s Law).

Lenz's Law illustration

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7. Examiner Guidance & Common Mistakes

Exam Strategy

• Defining Flux Density: Don’t be ambiguous about what is perpendicular. Explicitly state: “The force per unit current, per unit length on a wire placed at right angles to the magnetic field.”
• Lenz’s Law: If asked to explain the direction, do not just define the law. Apply it: “The induced current creates a field that opposes the change (e.g., magnet approaching).”
• Units: Always check units! $mT\to T$ ($\times 10^{-3}$), $c{m}^2\to m^2$ ($\times 10^{-4}$), $ms\to s$ ($\times 10^{-3}$).
• Graphs: If sketching induced e.m.f. from a changing flux graph, remember $\epsilon$ is proportional to the gradient of the flux graph. If the flux graph has a constant positive gradient, the e.m.f. is a constant negative value.
• Formula confusion: $F=BIL$ is for wires. $F=BQv$ is for isolated charges. Don’t mix them up.
• Hall Effect: When describing it, mention that the electric field set up by charge separation balances the magnetic force on the charge carriers.