Definition of Ferromagnetic Materials:
- Ferromagnetic materials are substances that exhibit strong magnetization when placed in an external magnetic field.
- These materials retain their magnetization even after the external field is removed.
- Common examples include iron (Fe), cobalt (Co), and nickel (Ni). Explanation of Ferromagnetism:
- The phenomenon of ferromagnetism arises due to the presence of magnetic domains.
- Each domain consists of a group of atomic dipoles aligned in the same direction.
- In an unmagnetized ferromagnetic material, these domains are randomly oriented, resulting in zero net magnetization.
Magnetic Domains and Alignment:
- When an external magnetic field is applied, the domains align in the direction of the field.
- The material becomes magnetized, and the alignment of the domains increases the overall magnetic moment. \[ B = \mu_0 (H + M) \] where:
- \( B \) = Magnetic field in the material
- \( H \) = Applied external field
- \( M \) = Magnetization of the material
- \( \mu_0 \) = Permeability of free space - In fully magnetized ferromagnetic materials, most domains align in the same direction, producing a strong magnetic effect.
Key Properties of Ferromagnetic Materials:
1. High Permeability: These materials have a high ability to concentrate magnetic flux.
2. Hysteresis Effect: The magnetization does not return to zero immediately after removing the field, leading to a hysteresis loop.
3. Curie Temperature (\( T_C \)): Above this temperature, the material loses its ferromagnetic properties and behaves as a paramagnet.
Conclusion:
- Ferromagnetic materials are widely used in applications like transformers, electromagnets, hard disks, and electric motors due to their ability to retain strong magnetization.
A current-carrying coil is placed in an external uniform magnetic field. The coil is free to turn in the magnetic field. What is the net force acting on the coil? Obtain the orientation of the coil in stable equilibrium. Show that in this orientation the flux of the total field (field produced by the loop + external field) through the coil is maximum.
Simar, Tanvi, and Umara were partners in a firm sharing profits and losses in the ratio of 5 : 6 : 9. On 31st March, 2024, their Balance Sheet was as follows:
Liabilities | Amount (₹) | Assets | Amount (₹) |
Capitals: | Fixed Assets | 25,00,000 | |
Simar | 13,00,000 | Stock | 10,00,000 |
Tanvi | 12,00,000 | Debtors | 8,00,000 |
Umara | 14,00,000 | Cash | 7,00,000 |
General Reserve | 7,00,000 | Profit and Loss A/c | 2,00,000 |
Trade Payables | 6,00,000 | ||
Total | 52,00,000 | Total | 52,00,000 |
Umara died on 30th June, 2024. The partnership deed provided for the following on the death of a partner:
If \(\begin{vmatrix} 2x & 3 \\ x & -8 \\ \end{vmatrix} = 0\), then the value of \(x\) is: