Question

What is hysteresis loss proportional to?

Answer 1

Hysteresis loss is proportional to the frequency of the magnetic field and the area of the hysteresis loop of the material. It also depends on the volume of the material and the magnetic properties of the material itself. The ultimate factor influencing hysteresis loss is the energy required to reverse the magnetic domains within the material.

Answer 2

Hysteresis loss occurs in magnetic materials when they are subjected to a cyclic magnetization process, like in transformers, electric motors, or inductors. When a material is magnetized, it retains some magnetization even after the external magnetizing field is removed. The energy used to overcome this residual magnetization results in hysteresis loss.

### Hysteresis Loss is Proportional To:

1. **Frequency of Magnetization (f):**
   - The hysteresis loss increases with the frequency of the magnetic cycles. Each cycle of magnetization and demagnetization causes a loss of energy, so more cycles per second (higher frequency) result in more energy lost.
   - Mathematically, hysteresis loss **increases linearly** with frequency.

2. **Volume of the Magnetic Material (V):**
   - The more material there is, the more energy is lost. Therefore, hysteresis loss is proportional to the volume of the magnetic core.
   - Larger cores have more material to magnetize and demagnetize, leading to higher losses.

3. **Magnetic Flux Density (B):**
   - The maximum magnetic flux density (also called peak flux density) indicates how strongly the material is magnetized. Higher flux densities cause more energy loss, because the magnetic domains within the material must rotate more, leading to increased energy dissipation.
   - Mathematically, hysteresis loss is proportional to the **nth power of magnetic flux density**, often approximated as:
     \[
     Hysteresis \ Loss \propto B_{max}^n
     \]
     where \(n\) is typically between 1.6 and 2.5, depending on the material.

4. **Hysteresis Coefficient (η or K_h):**
   - This is a constant that depends on the magnetic material itself and represents how easily a material undergoes magnetic domain alignment and reversal. For example, soft magnetic materials have low hysteresis loss, while hard magnetic materials have higher hysteresis loss.
   - Different materials like silicon steel, ferrites, or iron-nickel alloys have different hysteresis coefficients, which affect the overall loss.

### Formula for Hysteresis Loss:
The hysteresis loss can be expressed using the following formula:
\[
P_h = η \cdot B_{max}^n \cdot f \cdot V
\]
Where:
- \(P_h\) = Hysteresis loss (in watts)
- \(η\) or \(K_h\) = Hysteresis coefficient (depends on material)
- \(B_{max}\) = Maximum flux density
- \(f\) = Frequency of magnetization cycles
- \(V\) = Volume of the magnetic material

### Summary
Hysteresis loss is **proportional to the frequency of the magnetization cycle, the volume of the material, and the nth power of the maximum flux density**, where \(n\) typically varies between 1.6 and 2.5 based on the material's properties.