1. Concept: The electrical energy stored dynamically within a capacitor's field is proportional to the square of its voltage.
2. Formula: $$ U = \frac{1}{2} C V^2 $$
3. Solution: - Identify Capacitance: \( C = 20 \mu\text{F} = 20 \times 10^{-6} \text{ F} \).
- Identify Voltage: \( V = 200 \text{ V} = 2 \times 10^2 \text{ V} \).
- Square the voltage: \( V^2 = (200)^2 = 40000 = 4 \times 10^4 \).
- Substitute: \( U = \frac{1}{2} (20 \times 10^{-6}) (4 \times 10^4) \).
- Calculate: \( U = 10 \times 10^{-6} \times 4 \times 10^4 = 40 \times 10^{-2} \).
- Simplify: \( 40 \times 10^{-2} = 0.4 \text{ Joules} \).
4. Why other options are incorrect: Option A incorrectly ignores the micro (\( 10^{-6} \)) unit conversion prefix. Option B misses a decimal place order of magnitude shift.
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