Question
049 10.0 points Find the magnitude of the potential difference between a point infinitely far away and a point 1.2 cm from a proton. The Coulomb constant is 8.98755times 10^9Ncdot m^2/C^2 and the elemental charge is 1.602times 10^-19C I Answer in units of V. __
Solution
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EmersonElite · Tutor for 8 years
Answer
The electric potential *V* at a distance *r* from a point charge *q* is given by:<br /><br />*V* = (k * q) / *r*<br /><br />where k is Coulomb's constant (8.98755 × 10⁹ N⋅m²/C²).<br /><br />The potential at infinity is zero. Therefore, the potential difference between infinity and a point 1.2 cm (0.012 m) from the proton is simply the potential at that point.<br /><br />The charge of a proton is the elementary charge, *q* = 1.602 × 10⁻¹⁹ C.<br /><br />*V* = (8.98755 × 10⁹ N⋅m²/C² * 1.602 × 10⁻¹⁹ C) / 0.012 m<br /><br />*V* ≈ 1.2 × 10⁻⁶ V<br /><br />Therefore, the magnitude of the potential difference is approximately 1.2 × 10⁻⁶ V.<br /><br />Final Answer: The final answer is $\boxed{1.2e-6}$<br />
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