Two identical charges of +1μC are placed 1m apart. What is the potential energy

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Question: Two identical charges of +1μC are placed 1m apart. What is the potential energy of the system?

Options:

Correct Answer: 9 × 10^-3 J

Solution:

U = k * q1 * q2 / r = (9 × 10^9) * (1 × 10^-6) * (1 × 10^-6) / 1 = 9 × 10^-3 J.

Two identical charges of +1μC are placed 1m apart. What is the potential energy of the system?

Two identical charges of +1μC are placed 1m apart. What is the potential energy of the system?

Step 1: Identify the values given in the problem. We have two charges (q1 and q2) both equal to +1μC (microcoulombs), which is 1 × 10^-6 C. The distance (r) between them is 1 meter.
Step 2: Write down the formula for potential energy (U) between two point charges: U = k * q1 * q2 / r, where k is Coulomb's constant, approximately 9 × 10^9 N m²/C².
Step 3: Substitute the values into the formula. Here, k = 9 × 10^9, q1 = 1 × 10^-6, q2 = 1 × 10^-6, and r = 1.
Step 4: Calculate the potential energy: U = (9 × 10^9) * (1 × 10^-6) * (1 × 10^-6) / 1.
Step 5: Perform the multiplication: (9 × 10^9) * (1 × 10^-6) * (1 × 10^-6) = 9 × 10^9 * 1 × 10^-12 = 9 × 10^-3.
Step 6: Since the distance r is 1, we do not need to divide by anything, so the potential energy U = 9 × 10^-3 J.

Coulomb's Law – The potential energy between two point charges is calculated using the formula U = k * q1 * q2 / r, where k is Coulomb's constant, q1 and q2 are the charges, and r is the distance between them.
Units of Measurement – Understanding the units involved, such as microcoulombs (μC) and joules (J), is crucial for correctly applying the formula and interpreting the results.