What is the potential energy of a system of two charges +3 µC and +4 µC separate

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Question: What is the potential energy of a system of two charges +3 µC and +4 µC separated by 0.3 m? (2023)

Options:

Correct Answer: 0.36 J

Exam Year: 2023

Solution:

Potential energy U = k * q1 * q2 / r = (9 × 10^9 N m²/C²) * (3 × 10^-6 C) * (4 × 10^-6 C) / 0.3 m = 0.36 J.

What is the potential energy of a system of two charges +3 µC and +4 µC separated by 0.3 m? (2023)

What is the potential energy of a system of two charges +3 µC and +4 µC separated by 0.3 m? (2023)

Step 1: Identify the values given in the problem. We have two charges: q1 = +3 µC (microcoulombs) and q2 = +4 µC. Convert these to coulombs: q1 = 3 × 10^-6 C and q2 = 4 × 10^-6 C.
Step 2: Identify the distance between the charges, which is given as r = 0.3 m.
Step 3: Use the formula for potential energy (U) of two point charges: U = k * q1 * q2 / r, where k is the Coulomb's constant, approximately 9 × 10^9 N m²/C².
Step 4: Substitute the values into the formula: U = (9 × 10^9 N m²/C²) * (3 × 10^-6 C) * (4 × 10^-6 C) / (0.3 m).
Step 5: Calculate the numerator: (9 × 10^9) * (3 × 10^-6) * (4 × 10^-6) = 108 × 10^-3 = 0.108 J.
Step 6: Divide the result by the distance (0.3 m): U = 0.108 J / 0.3 = 0.36 J.
Step 7: Conclude that the potential energy of the system of two charges is 0.36 J.

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