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

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

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.

Steps: 8

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.