(c) (i) Define each of the following with respect to magnetic circuits: (ii) susceptibility; hysteresis. (2 marks) (d) A magnetic material has a relative permeability of 3. The material is placed in a magnetic field strength of 8 A/m. Determine the: (i) magnetic flux density in the material; (ii) magnetization; (iii) susceptibility. (6 marks)
Answer (1)
Defined susceptibility as the degree to which a material becomes magnetized in response to a magnetic field.
Defined hysteresis as the lagging of magnetization behind the magnetizing field.
Calculated magnetic flux density: B = μ 0 μ r H = 3.0159 × 1 0 − 5 T .
Calculated susceptibility: χ m = μ r − 1 = 2 .
Calculated magnetization: M = χ m H = 16 A/m .
The final answers are: B = 3.0159 × 1 0 − 5 T , χ m = 2 , M = 16 A/m .
Explanation
Problem Analysis We are given a problem related to magnetic circuits. We need to define susceptibility and hysteresis, and then calculate magnetic flux density, magnetization, and susceptibility for a given magnetic material.
Definition of Susceptibility Susceptibility is the degree to which a material will become magnetized in response to an applied magnetic field.
Definition of Hysteresis Hysteresis is the lagging of the magnetization of a ferromagnetic material behind variations of the magnetizing field.
Given Values We are given that the relative permeability, μ r = 3 , and the magnetic field strength, H = 8 A/m . We need to find the magnetic flux density B , the magnetization M , and the susceptibility χ m .
Calculating Magnetic Flux Density The magnetic flux density B is calculated using the formula B = μ 0 μ r H , where μ 0 = 4 π × 1 0 − 7 H/m is the permeability of free space. Substituting the given values, we have: B = ( 4 π × 1 0 − 7 H/m ) × 3 × ( 8 A/m ) B = 3.0159 × 1 0 − 5 T Therefore, the magnetic flux density is 3.0159 × 1 0 − 5 Tesla.
Calculating Susceptibility The susceptibility χ m is related to the relative permeability by the formula μ r = 1 + χ m . Therefore, χ m = μ r − 1 . Substituting the given value, we have: χ m = 3 − 1 = 2 Therefore, the susceptibility is 2.
Calculating Magnetization The magnetization M is calculated using the formula M = χ m H . Substituting the calculated susceptibility and the given magnetic field strength, we have: M = 2 × ( 8 A/m ) = 16 A/m Therefore, the magnetization is 16 A/m.
Final Answer The magnetic flux density in the material is 3.0159 × 1 0 − 5 T, the magnetization is 16 A/m, and the susceptibility is 2.
Examples
Understanding magnetic properties is crucial in designing transformers and inductors. For example, knowing the susceptibility of a core material helps engineers predict how well the core will enhance the magnetic field produced by a coil. Similarly, understanding hysteresis losses is essential for minimizing energy dissipation in AC applications. These calculations ensure efficient and reliable performance of electromagnetic devices.
