Magnetic Flux Density Formula
Calculate magnetic flux density using B = Φ/A.
Learn the relationship between magnetic flux and area with worked examples.
The Formula
Magnetic flux density (B) measures the strength of a magnetic field passing through a given area. It tells you how concentrated the magnetic field lines are in a region of space.
A stronger magnet or a smaller area both result in higher flux density. This quantity is essential in designing electric motors, generators, transformers, and MRI machines.
The SI unit of magnetic flux density is the tesla (T), named after Nikola Tesla. One tesla equals one weber per square meter (1 T = 1 Wb/m²).
Variables
| Symbol | Meaning | Unit |
|---|---|---|
| B | Magnetic flux density (field strength) | T (tesla) |
| Φ | Magnetic flux — total magnetic field passing through the surface | Wb (weber) |
| A | Cross-sectional area perpendicular to the field | m² |
Key Relationships
The formula can be rearranged:
- Flux density: B = Φ / A
- Magnetic flux: Φ = B × A
- Area: A = Φ / B
When the field is not perpendicular to the surface, the general form is Φ = B × A × cos θ, where θ is the angle between the field direction and the surface normal.
Example 1
A magnetic flux of 0.05 Wb passes through a coil with an area of 0.02 m². What is the flux density?
Identify values: Φ = 0.05 Wb, A = 0.02 m²
Apply the formula: B = Φ / A = 0.05 / 0.02
B = 2.5 T (a very strong magnetic field, similar to an MRI scanner)
Example 2
A solenoid produces a uniform field of 0.8 T. The cross-section has a radius of 3 cm. What is the total magnetic flux?
Calculate the area: A = πr² = π × (0.03)² = 2.827 × 10⁻³ m²
Rearrange to find flux: Φ = B × A = 0.8 × 2.827 × 10⁻³
Φ ≈ 2.26 × 10⁻³ Wb = 2.26 mWb
When to Use It
- Designing electric motors and generators
- Calculating transformer core requirements
- MRI machine magnetic field specifications
- Electromagnetic shielding calculations
- Any problem involving magnetic fields through a surface