Find dimension formula of polarisation ?

Options

A. `[L^(-2)T^(1)A^(1)]`
B. `[L^(2) T^(1)A^(-1)]`
C. `[L^(2)T^(1)A^(1)]`
D. `[L^(-3)T^(-1)A^(1)]`

Explanation

To find the dimension formula of polarization, we will follow these steps:

### Step 1: Understand the Definition of Polarization
Polarization (P) is defined as the dipole moment per unit volume. Mathematically, it can be expressed as:
\[ P = \frac{p}{V} \]
where \( p \) is the dipole moment and \( V \) is the volume.

### Step 2: Determine the Dipole Moment
The dipole moment (p) is defined as the product of charge (q) and the distance (d) between the charges:
\[ p = q \cdot d \]

### Step 3: Identify the Dimensions of Charge and Distance
- The dimension of charge (q) is represented as [A][T], where:
- [A] is the dimension of electric current.
- [T] is the dimension of time.

- The dimension of distance (d) is represented as [L], where [L] is the dimension of length.

### Step 4: Combine the Dimensions of Dipole Moment
Now, substituting the dimensions of charge and distance into the dipole moment:
\[ [p] = [q] \cdot [d] = [A][T] \cdot [L] = [A][L][T] \]

### Step 5: Determine the Dimension of Volume
The volume (V) is given by:
\[ V = L^3 \]
Thus, the dimension of volume is:
\[ [V] = [L]^3 \]

### Step 6: Find the Dimension of Polarization
Now, substituting the dimensions of dipole moment and volume into the formula for polarization:
\[ [P] = \frac{[p]}{[V]} = \frac{[A][L][T]}{[L]^3} \]

### Step 7: Simplify the Expression
Simplifying the expression gives:
\[ [P] = [A][L]^{1-3}[T] = [A][L]^{-2}[T] \]

### Final Answer
Thus, the dimension formula of polarization is:
\[ [P] = [A][L]^{-2}[T] \]

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