Solved Examples of Hysteresis Loop Analysis

📚 Quick Study Guide

• 🧲 Hysteresis refers to the lagging of magnetization behind the magnetizing field.
• 📈 A hysteresis loop visually represents the relationship between the magnetic field strength ($H$) and the magnetization ($M$ or $B$) of a ferromagnetic material.
• 🧱 Retentivity (Remanence): The magnetization ($B_r$) remaining in the material when the magnetic field is reduced to zero.
• 🚫 Coercivity: The magnetic field strength ($H_c$) required to bring the magnetization of the material to zero after it has been magnetized.
• 🔄 The area within the hysteresis loop represents the energy loss per cycle due to hysteresis. This energy loss is given by $\oint H dB$.
• 🌡️ The shape and size of the hysteresis loop depend on the material's properties, temperature, and applied field.
• 🔩 Materials with large hysteresis loops are suitable for permanent magnets (high retentivity and coercivity).
• 💾 Materials with small hysteresis loops are suitable for transformer cores (low energy loss).

Practice Quiz

1. What does the area enclosed by a hysteresis loop represent?
   1. A) The material's permeability.
   2. B) The energy loss per cycle due to hysteresis.
   3. C) The saturation magnetization.
   4. D) The material's coercivity.
2. What is 'retentivity' in the context of a hysteresis loop?
   1. A) The magnetic field strength required to demagnetize the material.
   2. B) The maximum magnetization achieved by the material.
   3. C) The magnetization remaining when the magnetic field is zero.
   4. D) The initial magnetization of the material.
3. Which of the following materials is most suitable for creating a permanent magnet?
   1. A) A material with a small hysteresis loop.
   2. B) A material with a large hysteresis loop.
   3. C) A material with zero coercivity.
   4. D) A material with zero retentivity.
4. What is 'coercivity' in the context of a hysteresis loop?
   1. A) The maximum magnetic field strength applied to the material.
   2. B) The magnetic field strength required to bring the magnetization to zero.
   3. C) The magnetization remaining when the external field is at its maximum.
   4. D) The rate at which magnetization changes with the applied field.
5. If a material has a high retentivity and high coercivity, what can we say about its hysteresis loop?
   1. A) It has a narrow and short loop.
   2. B) It has a wide and tall loop.
   3. C) It is a straight line.
   4. D) It doesn't have a loop.
6. Which of the following is NOT a factor affecting the shape of the hysteresis loop?
   1. A) Material properties.
   2. B) Temperature.
   3. C) Applied magnetic field.
   4. D) The material's color.
7. For a transformer core, which type of hysteresis loop is preferred?
   1. A) Large hysteresis loop
   2. B) Small hysteresis loop
   3. C) Square hysteresis loop
   4. D) Hysteresis loop with high retentivity