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 \( \lambda \), we can follow these steps:

### Step 1: Understand the Definition of Linear Charge Density
Linear charge density \( \lambda \) is defined as the amount of charge per unit length. Mathematically, it is expressed as:
\[ \lambda = \frac{Q}{L} \]
where \( Q \) is the charge and \( L \) is the length.

### Step 2: Write the Dimensional Formula for Charge
The dimensional formula for electric charge \( Q \) is given in terms of current and time. The current \( I \) has the dimensional formula:
\[ [I] = A \quad (\text{Ampere}) \]
Since charge is current multiplied by time, we have:
\[ [Q] = [I][T] = A \cdot T \]

### Step 3: Write the Dimensional Formula for Length
The dimensional formula for length \( L \) is simply:
\[ [L] = L \]

### Step 4: Substitute the Dimensional Formulas into the Expression for \( \lambda \)
Now, substituting the dimensional formulas for charge and length into the expression for linear charge density:
\[ [\lambda] = \frac{[Q]}{[L]} = \frac{A \cdot T}{L} \]

### Step 5: Simplify the Expression
This simplifies to:
\[ [\lambda] = A \cdot T \cdot L^{-1} \]

### Step 6: Write the Final Dimensional Formula
Thus, the dimensional formula for linear charge density \( \lambda \) is:
\[ [\lambda] = M^0 L^{-1} T^{1} A^{1} \]

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