Intensity of Magnetization has the same dimensions as

Options

A. Magnetic susceptibility
B. Magnetic moment
C. Intensity of magnetizing field
D. Magnetic permeability

Answer

To solve the question of which quantity has the same dimensions as the intensity of magnetization, we will follow these steps:

### Step 1: Understand the Definition of Intensity of Magnetization
The intensity of magnetization (I) is defined as the magnetic moment (m) per unit volume (V). Mathematically, it can be expressed as:
\[ I = \frac{m}{V} \]

### Step 2: Determine the Dimensions of Magnetic Moment
The magnetic moment (m) can be expressed as:
\[ m = I \cdot A \]
where:
- I is the current (with dimensions [A] or [I])
- A is the area (with dimensions [L^2])

Thus, the dimensions of magnetic moment are:
\[ [m] = [I] \cdot [L^2] = [A] \cdot [L^2] \]

### Step 3: Determine the Dimensions of Volume
The volume (V) has dimensions given by:
\[ [V] = [L^3] \]

### Step 4: Calculate the Dimensions of Intensity of Magnetization
Now, substituting the dimensions of magnetic moment and volume into the equation for intensity of magnetization:
\[ [I] = \frac{[m]}{[V]} = \frac{[A] \cdot [L^2]}{[L^3]} = [A] \cdot [L^{-1}] \]

So, the dimensions of intensity of magnetization are:
\[ [I] = [A] \cdot [L^{-1}] \]

### Step 5: Compare with Given Options
Now, we need to compare the dimensions of intensity of magnetization with the dimensions of the given options:

1. **Magnetic Susceptibility (χ)**: This is dimensionless (no dimensions).
2. **Magnetic Moment (m)**: As calculated, has dimensions of [A][L^2].
3. **Intensity of Magnetizing Field (H)**: The dimensions are [A][L^{-1}].
4. **Magnetic Permeability (μ)**: The dimensions are [M][L][T^{-2}][A^{-2}].

### Step 6: Identify the Correct Option
From the comparison, we see that the intensity of magnetizing field (H) has the same dimensions as the intensity of magnetization (I):
\[ [H] = [A] \cdot [L^{-1}] \]

Thus, the correct answer is:
**Intensity of Magnetizing Field (H)**.

### Final Answer:
Intensity of Magnetization has the same dimensions as **Intensity of Magnetizing Field**.

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