The dimensional formula of linear charge density `lambda` is

Options

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

Answer

To find the dimensional formula of linear charge density (λ), we need to understand what linear charge density represents. Linear charge density is defined as the charge per unit length.

### Step-by-Step Solution:

1. **Define Linear Charge Density**:
\[ \lambda = \frac{Q}{L} \]
where \( Q \) is the charge and \( L \) is the length.

2. **Find the Dimensional Formula of Charge (Q)**:
Charge \( Q \) can be expressed in terms of current \( I \) and time \( t \):
\[ Q = I \cdot t \]
The dimensional formula for current \( I \) is \( [I] = A \) (Ampere), and for time \( t \) it is \( [t] = T \). Therefore, the dimensional formula for charge \( Q \) becomes:
\[ [Q] = [I][t] = A \cdot T \]

3. **Find the Dimensional Formula of Length (L)**:
The dimensional formula for length \( L \) is:
\[ [L] = L \]

4. **Substitute into the Formula for λ**:
Now, substituting the dimensional formulas for \( Q \) and \( L \) into the equation for \( \lambda \):
\[ [\lambda] = \frac{[Q]}{[L]} = \frac{A \cdot T}{L} \]

5. **Express the Dimensional Formula**:
This can be expressed as:
\[ [\lambda] = A \cdot T \cdot L^{-1} \]
or in a more standard form:
\[ [\lambda] = M^0 \cdot L^{-1} \cdot T^1 \cdot A^1 \]

### Final Answer:
The dimensional formula of linear charge density \( \lambda \) is:
\[ M^0 L^{-1} T^1 A^1 \]