The dimensional formula of electric flux is

Options

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

Explanation

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

### Step 1: Understand the definition of electric flux
Electric flux (Φ) is defined as the product of the electric field (E) and the area (A) through which the field lines pass. Mathematically, this can be expressed as:
\[ \Phi = E \cdot A \]

### Step 2: Determine the dimensional formula for electric field
Electric field (E) can be defined in terms of force (F) and charge (Q). The relationship is given by:
\[ E = \frac{F}{Q} \]
The dimensional formula for force (F) is derived from Newton's second law, which states that force is mass (M) times acceleration (a). Thus, the dimensional formula for force is:
\[ [F] = M L T^{-2} \]

### Step 3: Determine the dimensional formula for area
The area (A) is given by the square of the length (L). Therefore, the dimensional formula for area is:
\[ [A] = L^2 \]

### Step 4: Determine the dimensional formula for charge
Charge (Q) can be expressed in terms of current (I) and time (T). The relationship is:
\[ Q = I \cdot T \]
Thus, the dimensional formula for charge is:
\[ [Q] = A T \]

### Step 5: Substitute the dimensional formulas into the equation for electric flux
Now, substituting the dimensional formulas into the equation for electric flux:
\[ \Phi = E \cdot A = \left(\frac{F}{Q}\right) \cdot A \]
Substituting the dimensional formulas:
\[ [\Phi] = \left[\frac{M L T^{-2}}{A T}\right] \cdot [L^2] \]

### Step 6: Simplify the expression
Now, simplifying the expression:
\[ [\Phi] = \frac{M L T^{-2}}{A T} \cdot L^2 = \frac{M L^3 T^{-2}}{A T} = \frac{M L^3}{A T^3} \]
Thus, we can express the dimensional formula for electric flux as:
\[ [\Phi] = M^1 L^3 T^{-3} A^{-1} \]

### Final Answer
The dimensional formula of electric flux is:
\[ \Phi = M^1 L^3 T^{-3} A^{-1} \]

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