Two identical charges are placed 1m apart. If the force between them is 9N, what

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Question: Two identical charges are placed 1m apart. If the force between them is 9N, what is the magnitude of each charge?

Options:

Correct Answer: 2μC

Solution:

Using Coulomb\'s law, F = k * |q1 * q2| / r². Let q be the charge, then 9 = (9 × 10^9) * (q²) / (1)². Solving gives q = 3μC.

Two identical charges are placed 1m apart. If the force between them is 9N, what is the magnitude of each charge?

Two identical charges are placed 1m apart. If the force between them is 9N, what is the magnitude of each charge?

Step 1: Understand that we are using Coulomb's law, which states that the force (F) between two charges is given by the formula F = k * |q1 * q2| / r².
Step 2: Identify the variables in the formula. Here, F is the force (9N), k is Coulomb's constant (approximately 9 × 10^9 N m²/C²), q1 and q2 are the charges (which are identical, so we can call them both q), and r is the distance between the charges (1m).
Step 3: Substitute the known values into the formula. Since both charges are the same, we can write it as 9 = (9 × 10^9) * (q * q) / (1)².
Step 4: Simplify the equation. This becomes 9 = (9 × 10^9) * q².
Step 5: To isolate q², divide both sides by (9 × 10^9). This gives q² = 9 / (9 × 10^9).
Step 6: Calculate the right side. This simplifies to q² = 1 / (10^9).
Step 7: Take the square root of both sides to find q. This gives q = √(1 / (10^9)).
Step 8: Simplify the square root. This results in q = 1 / (10^4) = 0.000001 C, which is equal to 3μC.

Coulomb's Law – Coulomb's law describes the electrostatic force between two charged objects, stating that the force is proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between them.
Identical Charges – The problem involves two identical charges, which simplifies the calculation since both charges are equal.
Unit Conversion – Understanding the conversion between microcoulombs (μC) and coulombs (C) is essential for correctly interpreting the final answer.