The dimensional formula of electric potential is

Options

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

Explanation

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

### Step 1: Understand the relationship between electric potential and electric field
Electric potential (V) is related to electric field (E) and distance (D) by the equation:
\[ V = E \times D \]

### Step 2: Write down the dimensions of distance
The dimensional formula for distance (D) is:
\[ [D] = L \]
where \( L \) represents length.

### Step 3: Find the dimensional formula for electric field
Electric field (E) can be defined in terms of force (F) and charge (Q):
\[ E = \frac{F}{Q} \]

### Step 4: Write down the dimensions of force
Force (F) is defined by Newton's second law:
\[ F = m \times a \]
where \( m \) is mass and \( a \) is acceleration. The dimensional formula for mass is:
\[ [m] = M \]
And the dimensional formula for acceleration (a) is:
\[ [a] = \frac{L}{T^2} \]
Thus, the dimensional formula for force is:
\[ [F] = M \times \frac{L}{T^2} = MLT^{-2} \]

### Step 5: Write down the dimensions of charge
The dimensional formula for electric charge (Q) is:
\[ [Q] = I \times T \]
where \( I \) is electric current and \( T \) is time.

### Step 6: Substitute the dimensions into the electric field formula
Now substituting the dimensions of force and charge into the electric field formula:
\[ [E] = \frac{[F]}{[Q]} = \frac{MLT^{-2}}{IT} = \frac{ML}{IT^2} \]

### Step 7: Substitute the dimensions of electric field and distance into the electric potential formula
Now substituting the dimensions of electric field and distance into the formula for electric potential:
\[ [V] = [E] \times [D] = \left(\frac{ML}{IT^2}\right) \times L = \frac{ML^2}{IT^2} \]

### Conclusion
Therefore, the dimensional formula of electric potential (V) is:
\[ [V] = \frac{ML^2}{IT^2} \]

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