1. Concept: The total electrical energy stored entirely within a region of space is dictated by its energy density, which scales with the square of the local electric field.
2. Formula: $$ U = \frac{1}{2} \epsilon_0 E^2 (A \cdot d) $$
3. Solution: - The energy equation proves that potential energy (\( U \)) is directly proportional to the square of the electric field intensity (\( E^2 \)).
- If the new field is \( 2E \), substituting it yields \( (2E)^2 = 4E^2 \).
- The entire system's total stored energy increases by a factor of 4, quadrupling.
4. Why other options are incorrect: Option A assumes a false linear relationship (\( U \propto E \)). Options B and C describe mathematically inverse relationships that apply to distance, not field strength.
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