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

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.

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