If γ is the susceptibility and μr is the relative permeability of a ferromagnetic substance, then
If γ is the susceptibility and μr is the relative permeability of a ferromagnetic substance, then
$\chi \ll 1$.
μr << 1
μr = 0
$\chi \gg 1$.
The Correct Option is D
Solution and Explanation
To solve the problem, we need to relate the magnetic susceptibility $\chi$ and the relative permeability $\mu_r$ for a ferromagnetic substance.
1. Understanding the Relationship:
For any magnetic material, the relationship between relative permeability $\mu_r$ and magnetic susceptibility $\chi$ is given by:
$\mu_r = 1 + \chi$
2. Behavior of Ferromagnetic Materials:
Ferromagnetic substances have a very high value of susceptibility $\chi$, which means they are strongly magnetized in the presence of a magnetic field.
Therefore, for ferromagnetic substances:
$\chi \gg 1$
So, $\mu_r = 1 + \chi \gg 1$
3. Eliminating Incorrect Options:
- Option 1: $\chi \ll 1$ → Incorrect (this is true for diamagnetic or weak paramagnetic materials)
- Option 2: $\mu_r \ll 1$ → Incorrect (this is never true for ferromagnetic materials)
- Option 3: $\mu_r = 0$ → Incorrect (this would imply the material does not respond to magnetic field)
- Option 4: $\chi \gg 1$ → Correct
Final Answer:
For ferromagnetic materials, $\chi \gg 1$.
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Concepts Used:
Magnetic Field
The magnetic field is a field created by moving electric charges. It is a force field that exerts a force on materials such as iron when they are placed in its vicinity. Magnetic fields do not require a medium to propagate; they can even propagate in a vacuum. Magnetic field also referred to as a vector field, describes the magnetic influence on moving electric charges, magnetic materials, and electric currents.
A magnetic field can be presented in two ways.
- Magnetic Field Vector: The magnetic field is described mathematically as a vector field. This vector field can be plotted directly as a set of many vectors drawn on a grid. Each vector points in the direction that a compass would point and has length dependent on the strength of the magnetic force.
- Magnetic Field Lines: An alternative way to represent the information contained within a vector field is with the use of field lines. Here we dispense with the grid pattern and connect the vectors with smooth lines.
Properties of Magnetic Field Lines
- Magnetic field lines never cross each other
- The density of the field lines indicates the strength of the field
- Magnetic field lines always make closed-loops
- Magnetic field lines always emerge or start from the north pole and terminate at the south pole.