Here is the step-by-step breakdown regarding the SI unit of magnetic flux.

### 1. The SI Unit and Its Name
The SI unit of magnetic flux is the **weber**.
*   **Symbol:** $\text{Wb}$
*   **Named After:** It is named after the German physicist and mathematician **Wilhelm Eduard Weber** (1804–1891), who made significant contributions to the study of electromagnetism.

### 2. Derivation in SI Base Units
To express the weber in terms of SI base units, we can use the definition of magnetic flux ($\Phi_B$) related to Faraday's Law of Induction.

**Step 1: Relate Flux to Voltage and Time**
According to Faraday's Law, the induced electromotive force (voltage, $V$) is equal to the rate of change of magnetic flux ($\Phi_B$) over time ($t$):
$$ V = \frac{d\Phi_B}{dt} \implies \Phi_B = V \cdot t $$
Therefore, the unit of magnetic flux is the **Volt-second** ($\text{V} \cdot \text{s}$).

**Step 2: Break down the Volt ($\text{V}$)**
The volt is a derived unit defined as energy per unit charge:
$$ 1 \, \text{V} = 1 \, \frac{\text{Joule}}{\text{Coulomb}} = \frac{\text{J}}{\text{C}} $$

**Step 3: Break down the Joule ($\text{J}$) and Coulomb ($\text{C}$)**
*   **Joule (Energy):** Work is force times distance.
    $$ 1 \, \text{J} = 1 \, \text{N} \cdot \text{m} = (1 \, \text{kg} \cdot \text{m}/\text{s}^2) \cdot \text{m} = 1 \, \text{kg} \cdot \text{m}^2 \cdot \text{s}^{-2} $$
*   **Coulomb (Charge):** Charge is current times time.
    $$ 1 \, \text{C} = 1 \, \text{A} \cdot \text{s} $$

**Step 4: Combine to find the Volt**
Substitute the base units back into the expression for the Volt:
$$ 1 \, \text{V} = \frac{1 \, \text{kg} \cdot \text{m}^2 \cdot \text{s}^{-2}}{1 \, \text{A} \cdot \text{s}} = 1 \, \text{kg} \cdot \text{m}^2 \cdot \text{s}^{-3} \cdot \text{A}^{-1} $$

**Step 5: Calculate the Weber ($\text{V} \cdot \text{s}$)**
Finally, multiply the Volt by the second ($\text{s}$) to get the Weber:
$$ 1 \, \text{Wb} = 1 \, \text{V} \cdot \text{s} = (\text{kg} \cdot \text{m}^2 \cdot \text{s}^{-3} \cdot \text{A}^{-1}) \cdot \text{s} $$
$$ 1 \, \text{Wb} = \text{kg} \cdot \text{m}^2 \cdot \text{s}^{-2} \cdot \text{A}^{-1} $$

***

### Final Conclusion

*   **SI Unit:** Weber ($\text{Wb}$)
*   **Named After:** Wilhelm Eduard Weber
*   **SI Base Units:**
    $$ \text{kg} \cdot \text{m}^2 \cdot \text{s}^{-2} \cdot \text{A}^{-1} $$