Magnetic Properties Of Materials

The root mean square (rms) velocity of gas molecules is given by the formula:
where: - is the Boltzmann constant,
- is the absolute temperature in Kelvin,
- is the mass of the gas molecule.
The ratio of the rms velocities at two different temperatures and can be written as: Given: - ,
- .
Substitute these values into the formula for the ratio of rms velocities: Thus, the ratio of the rms velocities is:

The dimensions of each quantity are as follows: - (magnetic moment) has the dimension of - (magnetic field) has the dimension of - (Boltzmann constant) has the dimension of - (temperature) has the dimension of Thus, the overall dimension of is: Simplifying, we get:

Step 1: Understanding the Concept:
Diamagnetic materials are weakly repelled by magnetic fields (e.g., Hg, Cu, Bi). Paramagnetic materials are weakly attracted (e.g., Ca, Al, Pt).

Step 2: Detailed Explanation:
Hg (mercury) is diamagnetic. Ca (calcium) is paramagnetic.

Step 3: Final Answer:
Diamagnetic: Hg, Paramagnetic: Ca.

Concept:

Step 1: Substitute.


Step 2: Interpretation.
Negative susceptibility diamagnetic material.

Step 1: Understanding the Concept:
Magnetic materials are broadly classified into three main categories based on their behavioral response in an external magnetic field: diamagnetic, paramagnetic, and ferromagnetic.
Diamagnetic materials develop an induced magnetic dipole moment in a direction strictly opposite to the applied magnetic field and are thus weakly repelled by magnets.
Step 2: Key Formula or Approach:
Solving this problem primarily requires factual knowledge of common chemical elements and their standardized magnetic properties at normal room temperature.
Step 3: Detailed Explanation:
Let's systematically evaluate the magnetic nature of each given element option.
Option (E) Iron (Fe) and Option (C) Cobalt (Co) are classic and well-known ferromagnetic materials.
Option (B) Gadolinium (Gd) is strongly ferromagnetic at low temperatures but transitions to paramagnetic at room temperature.
Option (D) Sodium (Na) is an alkali metal that typically exhibits paramagnetic properties.
Option (A) Bismuth (Bi) is fundamentally characterized as a strong diamagnetic material.
Step 4: Final Answer:
Bi (Bismuth) is the diamagnetic material.

Concept:
• Work done:

Step 1: First rotation
Given:

Step 2: Second rotation


Step 3: Ratio
Final Conclusion:
Option (D)

Concept:
• Self inductance:

Step 1: Given


Step 2: New inductance
Final Conclusion:
Option (E)