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 dimensional formula of polarization, we can follow these steps:

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

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

- The dimension of charge (q) is given by:
\[ [q] = [I][T] \]
where [I] is the dimension of electric current (Ampere) and [T] is the dimension of time.

- The dimension of distance (d) is:
\[ [d] = [L] \]

Thus, the dimensional formula for dipole moment (p) becomes:
\[ [p] = [q][d] = [I][T][L] \]

### Step 3: Determine the Dimensional Formula of Volume
The volume (V) is given by the cube of length:
\[ V = L^3 \]
Thus, the dimensional formula for volume is:
\[ [V] = [L^3] \]

### Step 4: Combine the Dimensional Formulas
Now, we can substitute the dimensional formulas of dipole moment and volume into the formula for polarization:
\[ [P] = \frac{[p]}{[V]} = \frac{[I][T][L]}{[L^3]} \]

### Step 5: Simplify the Expression
When we simplify the expression, we get:
\[ [P] = [I][T][L^{-2}] \]

### Final Answer
Thus, the dimensional formula for polarization is:
\[ [P] = [I][T][L^{-2}] \]