What is b and h in a hysteresis loop?
2 Answers
In a hysteresis loop, commonly associated with magnetic materials, "b" typically represents the magnetic flux density, often denoted as \( B \). "h" usually stands for the magnetic field strength, denoted as \( H \). The hysteresis loop graphically represents the relationship between these two quantities as the magnetic material is subjected to varying external magnetic fields. Would you like to delve deeper into the significance of this loop?
In the context of a hysteresis loop for magnetic materials, **B** and **H** represent two key physical quantities related to magnetism:
### 1. **B** – Magnetic Flux Density (Magnetic Induction):
- **Symbol**: \( \mathbf{B} \)
- **Unit**: Tesla (T) or Weber per square meter (Wb/m²)
- **Definition**: Magnetic flux density, or magnetic induction, is the amount of magnetic flux through a given area in a material. It represents the strength of the magnetic field inside the material. It accounts for the effects of both the applied magnetic field and the material's internal magnetization.
- Mathematically, it's defined as:
\[
\mathbf{B} = \mu_0 (\mathbf{H} + \mathbf{M})
\]
Where:
- \( \mu_0 \) is the permeability of free space.
- \( \mathbf{H} \) is the applied magnetic field strength.
- \( \mathbf{M} \) is the magnetization of the material.
### 2. **H** – Magnetic Field Strength (Magnetizing Force):
- **Symbol**: \( \mathbf{H} \)
- **Unit**: Ampere per meter (A/m)
- **Definition**: Magnetic field strength is the amount of magnetizing force applied to a magnetic material. It is the external magnetic field applied by a current or other external sources to magnetize the material.
- Mathematically, \( \mathbf{H} \) is related to the current and number of turns in a coil producing the field:
\[
\mathbf{H} = \frac{I}{l}
\]
Where:
- \( I \) is the current in the coil.
- \( l \) is the length of the solenoid or the path of the magnetic field.
### Hysteresis Loop Explained:
The hysteresis loop, also called the **B-H curve**, shows the relationship between the magnetic flux density (**B**) and the magnetic field strength (**H**) when a material is magnetized and then demagnetized.
Here’s what happens in a hysteresis loop:
1. **Initial Magnetization**: When an unmagnetized material is exposed to an increasing magnetic field (**H**), its magnetic flux density (**B**) increases and follows a certain path. This is called the initial magnetization curve.
2. **Saturation**: At a certain point, further increasing **H** won't cause much change in **B**. This state is called **saturation**, where the material is fully magnetized.
3. **Reducing H**: If **H** is reduced back to zero, the magnetic flux density **B** doesn't return to zero but rather remains at a certain value. This is called the **remanent magnetization** or **remanence** (\( B_r \)).
4. **Coercivity (Hc)**: To reduce **B** back to zero, the applied magnetic field **H** must be reversed and increased in the opposite direction. The value of **H** at which **B** becomes zero is called the **coercive field** or **coercivity** (\( H_c \)).
5. **Opposite Saturation**: As **H** continues to increase in the opposite direction, the material becomes magnetized in the reverse direction, and **B** reaches saturation in the opposite sense.
6. **Completing the Loop**: By returning **H** to its original direction, the hysteresis loop is completed, showing the energy loss (hysteresis loss) due to the magnetization and demagnetization process.
### Key Points in the B-H Curve:
- **Remanence (Br)**: The magnetic flux density left in the material when the magnetizing field is removed.
- **Coercivity (Hc)**: The magnetic field required to reduce the magnetization of the material to zero after saturation.
- **Saturation Point**: The point where further increases in the applied magnetic field do not significantly increase the magnetic flux density.
### Why the B-H Curve is Important:
- It represents **magnetic hysteresis**: the phenomenon that a material’s magnetic properties depend not only on the current magnetic field but also on its magnetic history.
- The loop area represents **energy loss** per cycle, which is crucial in understanding losses in transformers, motors, and other electromagnetic devices.
This relationship between **B** and **H** is critical in designing and understanding the behavior of magnetic materials in electrical engineering applications, such as transformers, inductors, and magnetic storage devices.
### 1. **B** – Magnetic Flux Density (Magnetic Induction):
- **Symbol**: \( \mathbf{B} \)
- **Unit**: Tesla (T) or Weber per square meter (Wb/m²)
- **Definition**: Magnetic flux density, or magnetic induction, is the amount of magnetic flux through a given area in a material. It represents the strength of the magnetic field inside the material. It accounts for the effects of both the applied magnetic field and the material's internal magnetization.
- Mathematically, it's defined as:
\[
\mathbf{B} = \mu_0 (\mathbf{H} + \mathbf{M})
\]
Where:
- \( \mu_0 \) is the permeability of free space.
- \( \mathbf{H} \) is the applied magnetic field strength.
- \( \mathbf{M} \) is the magnetization of the material.
### 2. **H** – Magnetic Field Strength (Magnetizing Force):
- **Symbol**: \( \mathbf{H} \)
- **Unit**: Ampere per meter (A/m)
- **Definition**: Magnetic field strength is the amount of magnetizing force applied to a magnetic material. It is the external magnetic field applied by a current or other external sources to magnetize the material.
- Mathematically, \( \mathbf{H} \) is related to the current and number of turns in a coil producing the field:
\[
\mathbf{H} = \frac{I}{l}
\]
Where:
- \( I \) is the current in the coil.
- \( l \) is the length of the solenoid or the path of the magnetic field.
### Hysteresis Loop Explained:
The hysteresis loop, also called the **B-H curve**, shows the relationship between the magnetic flux density (**B**) and the magnetic field strength (**H**) when a material is magnetized and then demagnetized.
Here’s what happens in a hysteresis loop:
1. **Initial Magnetization**: When an unmagnetized material is exposed to an increasing magnetic field (**H**), its magnetic flux density (**B**) increases and follows a certain path. This is called the initial magnetization curve.
2. **Saturation**: At a certain point, further increasing **H** won't cause much change in **B**. This state is called **saturation**, where the material is fully magnetized.
3. **Reducing H**: If **H** is reduced back to zero, the magnetic flux density **B** doesn't return to zero but rather remains at a certain value. This is called the **remanent magnetization** or **remanence** (\( B_r \)).
4. **Coercivity (Hc)**: To reduce **B** back to zero, the applied magnetic field **H** must be reversed and increased in the opposite direction. The value of **H** at which **B** becomes zero is called the **coercive field** or **coercivity** (\( H_c \)).
5. **Opposite Saturation**: As **H** continues to increase in the opposite direction, the material becomes magnetized in the reverse direction, and **B** reaches saturation in the opposite sense.
6. **Completing the Loop**: By returning **H** to its original direction, the hysteresis loop is completed, showing the energy loss (hysteresis loss) due to the magnetization and demagnetization process.
### Key Points in the B-H Curve:
- **Remanence (Br)**: The magnetic flux density left in the material when the magnetizing field is removed.
- **Coercivity (Hc)**: The magnetic field required to reduce the magnetization of the material to zero after saturation.
- **Saturation Point**: The point where further increases in the applied magnetic field do not significantly increase the magnetic flux density.
### Why the B-H Curve is Important:
- It represents **magnetic hysteresis**: the phenomenon that a material’s magnetic properties depend not only on the current magnetic field but also on its magnetic history.
- The loop area represents **energy loss** per cycle, which is crucial in understanding losses in transformers, motors, and other electromagnetic devices.
This relationship between **B** and **H** is critical in designing and understanding the behavior of magnetic materials in electrical engineering applications, such as transformers, inductors, and magnetic storage devices.