When point charges q1 = +8.9 μC and q2 = +7.6 μC are brought near each other, each experiences a repulsive force of magnitude 0.10 N. Determine the distance between the charges.
I got 6.08 m
Take the square root and you're there
To determine the distance between the charges, you can use Coulomb's Law, which states that the force between two point 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 the electrostatic constant (9 x 10^9 N m^2/C^2), q1 and q2 are the magnitudes of the charges, and r is the distance between the charges.
In this case, the force (F) is given as 0.10 N, q1 is +8.9 μC, and q2 is +7.6 μC.
Plugging in the values into the formula, we get:
0.10 N = (9 x 10^9 N m^2/C^2) * (|+8.9 μC * +7.6 μC| / r^2)
To simplify the calculation, let's convert the charges to coulombs:
8.9 μC = 8.9 x 10^-6 C
7.6 μC = 7.6 x 10^-6 C
Now, we can re-write the equation as:
0.10 N = (9 x 10^9 N m^2/C^2) * (|8.9 x 10^-6 C * 7.6 x 10^-6 C| / r^2)
Simplifying further:
0.10 N = (9 x 10^9 N m^2/C^2) * (67.64 x 10^-12 C^2 / r^2)
To isolate r, we divide both sides of the equation by the electrostatic constant and multiply by r^2:
0.10 N / (9 x 10^9 N m^2/C^2) = 67.64 x 10^-12 C^2 / r^2
r^2 = (67.64 x 10^-12 C^2) / (0.10 N / (9 x 10^9 N m^2/C^2))
r^2 = (67.64 x 10^-12 C^2) / (0.10 N / (9 x 10^9 N m^2/C^2))
r^2 = (67.64 x 10^-12 C^2) * ((9 x 10^9 N m^2/C^2) / 0.10 N)
Simplifying the calculation:
r^2 = 606.76 x 10^-3 m^3 / N
r^2 = 606.76 x 10^-3 m^3 / 0.10 x 10^3 N
r^2 = 606.76 x 10^-3 m^3 / 0.10 x 10^3 N
r^2 = 606.76 x 10^-3 m^3 / 10^-1 N
r^2 = 606.76 x 10^-3 m^3 / 10^-1 N
r^2 = (606.76 x 10^-3 m^3) / (10^-1 N)
r^2 = (606.76 x 10^-3 m^3) * (10 N)
r^2 = 606.76 x 10^-3 m^3 / N
Taking the square root of both sides, we get:
r = sqrt(606.76 x 10^-3) m
Calculating the value, we find:
r ≈ 0.779 m
Therefore, the distance between the charges is approximately 0.779 meters.
Your answer of 6.08 meters seems to be incorrect. Double-check your calculations to see where the mistake occurred.