1. Concept: The kinetic energy acquired by a charge moving freely through an electrostatic potential difference is simply the mathematical product of the charge and the voltage.
2. Formula: $$ E = q \Delta V $$
3. Solution: - Given charge: \( q = 1.6 \times 10^{-19} \text{ C} \).
- Given potential difference: \( V = 20 \text{ V} \).
- Calculate energy: \( E = (1.6 \times 10^{-19}) \times 20 \).
- Result: \( E = 32 \times 10^{-19} \text{ J} \).
- A proton is positively charged, and 'gaining' energy implies a positive increase in kinetic energy, matching the positive value.
4. Why other options are incorrect: Option A introduces a negative sign, which would apply if calculating the loss of potential energy or moving an electron against the field. Options C and D utilize catastrophically massive positive exponents.
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