recall and use Φ = BA

What is Magnetic Flux?

Think of magnetic flux as the “amount of magnetic field lines” that pass through a surface. If you imagine a fan blowing air, the amount of air that goes through a screen is like magnetic flux. The more field lines or the larger the area, the greater the flux.

The basic relationship is: $Φ = B A$ where $B$ = magnetic field strength (teslas, T) $A$ = area of the surface (m²). If the field is not perpendicular to the surface, we use the angle θ: $Φ = B A \cos θ$.

The Φ = BA Formula in Action

1. Identify the magnetic field strength $B$ (given or measured).
2. Measure the area $A$ of the loop or surface.
3. Check the orientation: if the field is perpendicular, θ = 0° and cosθ = 1.
4. Multiply: $Φ = B \times A$.

⚡ Quick Tip: If you’re given a coil with many turns, remember that the total flux linkage is $N Φ$ where $N$ is the number of turns.

Examples & Analogies

📐 Example 1: A square loop of side 0.1 m lies in a uniform field of 0.5 T perpendicular to the loop. Area: $A = (0.1\,\text{m})^2 = 0.01\,\text{m}^2$ Flux: $Φ = 0.5\,\text{T} \times 0.01\,\text{m}^2 = 0.005\,\text{Wb}$

🔄 Analogy: Imagine a river (magnetic field) flowing through a rectangular gate (area). The amount of water passing through the gate is the flux. If you tilt the gate, less water passes through – that’s the cosθ factor.

Exam Tips for 9702

• Always state the formula clearly: $Φ = B A \cos θ$.
• Check units: B in teslas (T), A in square metres (m²), Φ in webers (Wb).
• When a coil has N turns, remember the total flux linkage is $N Φ$.
• Use diagrams: sketch the field lines, the loop, and indicate the angle θ.
• For problems involving changing flux, remember Faraday’s law: $𝔈 = -\dfrac{dΦ}{dt}$.
• Practice converting between SI units (e.g., 1 T = 1 Wb/m²).

🚀 Remember: The key to success is understanding the relationship between the magnetic field, the area it passes through, and the orientation. Once you can calculate Φ quickly, you’ll be ready for any induction question!