The dimensional formula of electric intensity is

Options

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

Explanation

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

### Step 1: Understand the Definition of Electric Intensity
Electric intensity (E) is defined as the force (F) experienced by a unit charge (Q). Thus, we can express it mathematically as:
\[ E = \frac{F}{Q} \]

### Step 2: Determine the Dimensional Formula for Force
The dimensional formula for force can be derived from Newton's second law of motion, which states that force is equal to mass (m) multiplied by acceleration (a). The dimensional formula for mass is:
\[ [m] = M \]
The dimensional formula for acceleration is:
\[ [a] = \frac{[l]}{[t^2]} = \frac{L}{T^2} \]
Therefore, the dimensional formula for force (F) is:
\[ [F] = [m][a] = M \cdot \frac{L}{T^2} = MLT^{-2} \]

### Step 3: Determine the Dimensional Formula for Charge
Charge (Q) can be defined in terms of current (I) and time (t). The dimensional formula for current is:
\[ [I] = A \]
The dimensional formula for time is:
\[ [t] = T \]
Thus, the dimensional formula for charge (Q) is:
\[ [Q] = [I][t] = A \cdot T \]

### Step 4: Substitute the Dimensional Formulas into the Electric Intensity Formula
Now we can substitute the dimensional formulas for force and charge into the equation for electric intensity:
\[ [E] = \frac{[F]}{[Q]} = \frac{MLT^{-2}}{AT} \]

### Step 5: Simplify the Expression
To simplify the expression, we divide the dimensional formulas:
\[ [E] = \frac{MLT^{-2}}{AT} = \frac{M}{A} \cdot \frac{L}{T^2} \cdot \frac{1}{T} = \frac{M}{A} \cdot \frac{L}{T^3} \]
This can be rewritten as:
\[ [E] = M^1 L^1 T^{-3} A^{-1} \]

### Conclusion
Thus, the dimensional formula for electric intensity is:
\[ [E] = M^1 L^1 T^{-3} A^{-1} \]

### Final Answer
The correct option is:
**C: \( M^1 L^1 T^{-3} A^{-1} \)**

---