Two identical point charges are 0.3 m away from each other. Calculate the magnitude of the identical charges if their electric force is 3.0x10-7 N.Group of answer choices1.7x10^-9 C3x10^-9 uC1.7x10^-9 uC3x10^-18 C
Question
Two identical point charges are 0.3 m away from each other. Calculate the magnitude of the identical charges if their electric force is 3.0x10-7 N.Group of answer choices1.7x10^-9 C3x10^-9 uC1.7x10^-9 uC3x10^-18 C
Solution
To solve this problem, we can use Coulomb's Law, which states that the force between two charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. The formula for Coulomb's Law is:
F = k * q1 * q2 / r^2
where: F is the force between the charges, k is Coulomb's constant (8.99 * 10^9 N m^2/C^2), q1 and q2 are the charges (which are identical in this case), and r is the distance between the charges.
Given that F = 3.0 * 10^-7 N, r = 0.3 m, and q1 = q2, we can substitute these values into the formula and solve for q1:
3.0 * 10^-7 N = 8.99 * 10^9 N m^2/C^2 * q1^2 / (0.3 m)^2
Solving for q1 gives:
q1 = sqrt[(3.0 * 10^-7 N * (0.3 m)^2) / (8.99 * 10^9 N m^2/C^2)] q1 = sqrt[(9.0 * 10^-8 N m^2) / (8.99 * 10^9 N m^2/C^2)] q1 = sqrt[10^-17 C^2] q1 = 1.0 * 10^-9 C
Therefore, the magnitude of the identical charges is 1.0 * 10^-9 C. However, this option is not available in the given answer choices. There might be a mistake in the problem or the answer choices.
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