Step 1: Understanding the Concept:
Electric flux (\(\Phi_E\)) is a measure of the total electric field lines passing through a given area.
To find the base SI units, we must decompose the physical quantities involved into the seven fundamental SI units: Mass (\(kg\)), Length (\(m\)), Time (\(s\)), and Electric Current (\(A\)).
Step 2: Key Formula or Approach:
The definition of electric flux is:
\[ \Phi_E = E \times A \]
Where \(E\) is the electric field and \(A\) is the area.
The electric field is defined as force per unit charge:
\[ E = \frac{F}{q} \]
Combining these:
\[ \Phi_E = \frac{F \times A}{q} \]
Step 3: Detailed Explanation:
Let's find the base units for each component:
1. Force (F): From Newton's second law (\(F = ma\)), the units are \(kg \cdot m \cdot s^{-2}\).
2. Area (A): The unit is \(m^2\).
3. Charge (q): From \(I = q/t\), we have \(q = I \cdot t\). The units are \(A \cdot s\).
Now, substitute these into the flux equation:
\[ \text{Unit of } \Phi_E = \frac{(kg \cdot m \cdot s^{-2}) \cdot (m^2)}{A \cdot s} \]
Simplify the numerator:
\[ \text{Unit of } \Phi_E = \frac{kg \cdot m^3 \cdot s^{-2}}{A \cdot s} \]
Bring the units from the denominator to the numerator by changing the signs of their exponents:
\[ \text{Unit of } \Phi_E = kg \cdot m^3 \cdot s^{-2} \cdot s^{-1} \cdot A^{-1} \]
Group the time units:
\[ \text{Unit of } \Phi_E = kg \cdot m^3 \cdot s^{-3} \cdot A^{-1} \]
This matches Option (D).
Step 4: Final Answer:
The SI base unit of electric flux is \(kg m^3 s^{-3} A^{-1}\).