The dimensional formula for electric potential is

Options

A. `[M L^(2) T^(-3) A^(-1)]`
B. `[M L T^(-3) A^(-1)]`
C. `[M L^(2) T^(-3) K^(-1)]`
D. none of these

Explanation

To find the dimensional formula for electric potential, we can follow these steps:

### Step 1: Understand the definition of electric potential
Electric potential (V) is defined as the work done (W) per unit charge (Q) to move a charge from a reference point to a specific point in an electric field. Mathematically, this can be expressed as:
\[ V = \frac{W}{Q} \]

### Step 2: Determine the dimensions of work
Work (W) is defined as force (F) multiplied by distance (d):
\[ W = F \cdot d \]
The dimensional formula for force (F) is given by:
\[ F = m \cdot a \]
Where:
- \( m \) is mass (M)
- \( a \) is acceleration (L T^{-2})

Thus, the dimensional formula for force is:
\[ [F] = [M][L][T^{-2}] = M L T^{-2} \]

Now, substituting this into the formula for work:
\[ [W] = [F][d] = [M L T^{-2}][L] = M L^2 T^{-2} \]

### Step 3: Determine the dimensions of charge
The dimensional formula for electric charge (Q) is represented as:
\[ [Q] = A \cdot T \]
Where:
- \( A \) is the unit of electric current
- \( T \) is time

### Step 4: Combine the dimensions to find electric potential
Now, substituting the dimensions of work and charge into the formula for electric potential:
\[ [V] = \frac{[W]}{[Q]} = \frac{M L^2 T^{-2}}{A T} \]

This simplifies to:
\[ [V] = M L^2 T^{-3} A^{-1} \]

### Step 5: Conclusion
Thus, the dimensional formula for electric potential is:
\[ [V] = M L^2 T^{-3} A^{-1} \]