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Φ = BA cosθ

PHY051 · Magnetism · Class 12 + College

Magnetic flux

Objective: To understand magnetic flux through a loop and how it changes as the loop turns.

🧰 Apparatus

  • Wire loop on an axle
  • Uniform field (Helmholtz coils or magnet pair)
  • Flux meter or search coil with data logger

📐 Formulas and SI units

Φ = BA cos θ (Wb = T m²)

💡 Theory

Magnetic flux measures how much field passes through an area: Φ = BA cos θ, where θ is the angle between the field and the normal to the loop. It is largest when the loop faces the field and zero when the loop is edge-on. A turning loop has changing flux, which is how generators work.

🪜 Procedure

  1. Place the loop in the uniform field facing it (θ = 0).
  2. Measure the flux.
  3. Rotate the loop in 30° steps and record the flux.
  4. Plot Φ against θ: a cosine curve.

📋 Observations Simulated values

✅ Result and conclusion

0.2 T through 0.05 m² at 60° gives 5 mWb; the flux is zero at 90°.

🔬 In a real lab

Real fields are only uniform near the centre of the coils; search coils measure the change in flux, not flux itself.

⚠️ Safety

Strong magnets pinch fingers and wipe cards; keep them apart and away from devices.

❓ Quick check

1. Flux is zero when the loop is…

2. Unit of magnetic flux?

3. Turning a loop in a field changes the flux, which induces…

🏋️ Practice

EasyB = 0.5 T, A = 0.1 m², θ = 0. Φ?

Answer: 0.05 Wb

MediumSame at 60°?

Answer: 0.025 Wb

ChallengeΦ for θ = 180°?

Answer: −BA (reversed)