The dimensional formula for magnetising field `H` is

Options

A. `[M^(0) L^(-1) T^(0) A]`
B. `[M^(0) L T^(-3) A]`
C. `[M^(0) L TA^(-1)]`
D. `[M^(0) L^(1) T^(-1) A]`

Explanation

To find the dimensional formula for the magnetizing field \( H \), we can follow these steps:

### Step 1: Understand the relationship of \( H \)
The magnetizing field \( H \) is defined as the magnetic field \( B \) divided by the permeability \( \mu \):
\[ H = \frac{B}{\mu} \]

### Step 2: Find the dimensional formula for \( B \)
The magnetic field \( B \) can be expressed in terms of force \( F \), charge \( Q \), and velocity \( V \):
\[ B = \frac{F}{QV} \]
Where:
- The dimensional formula for force \( F \) is \( [F] = M L T^{-2} \).
- The charge \( Q \) has the dimensional formula \( [Q] = I T = A T \).
- The velocity \( V \) has the dimensional formula \( [V] = L T^{-1} \).

Now substituting these into the formula for \( B \):
\[ [B] = \frac{MLT^{-2}}{(AT)(LT^{-1})} = \frac{MLT^{-2}}{A T L T^{-1}} = \frac{MLT^{-2}}{A L T^{-1}} = M L^{0} T^{-2} A^{-1} \]

### Step 3: Find the dimensional formula for permeability \( \mu \)
The permeability \( \mu \) is defined as:
\[ \mu = \frac{B}{H} \]
The unit of permeability is Henry per meter, which can be expressed as:
\[ \mu = \frac{B}{H} \Rightarrow [\mu] = [B] [H]^{-1} \]
From the unit of Henry (H), we have:
\[ 1 \, \text{H} = 1 \, \frac{\text{kg}}{\text{A}^2 \cdot \text{s}^2} = M L T^{-2} A^{-2} \]
Thus, the dimensional formula for \( \mu \) is:
\[ [\mu] = M L T^{-2} A^{-2} \]

### Step 4: Calculate the dimensional formula for \( H \)
Now we can substitute the dimensional formulas for \( B \) and \( \mu \) back into the equation for \( H \):
\[ [H] = \frac{[B]}{[\mu]} = \frac{M L^{0} T^{-2} A^{-1}}{M L T^{-2} A^{-2}} \]
This simplifies to:
\[ [H] = \frac{M L^{0} T^{-2} A^{-1}}{M L T^{-2} A^{-2}} = M^{0} L^{-1} T^{0} A^{1} = L^{-1} A^{1} \]

### Final Result
Thus, the dimensional formula for the magnetizing field \( H \) is:
\[ [H] = L^{-1} A^{1} \]

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