recall and use Φ = BA

Electromagnetic Induction

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.

ParameterValue
\$B\$ (magnetic field)0.5 T
\$A\$ (area)0.01 m²
θ (angle)0° (perpendicular)
Φ (flux)0.005 Wb

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!