A small plastic sphere with a charge of -5.0 is near another small plastic sphere with a charge of -15 .
Part A -
If the spheres repel one another with a force of magnitude 8.3×10−4 , what is the distance between the spheres?
Express your answer using two significant figures.
force= k q1*q2/distance^2
You just have to cite units when you givenumbers.
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To find the distance between the spheres, we can use Coulomb's law, which states that the electrostatic force between two charged objects is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.
The equation for Coulomb's law is:
F = k * (q1 * q2) / r^2
Where:
F is the electrostatic force,
k is the Coulomb's constant,
q1 and q2 are the charges on the spheres, and
r is the distance between the spheres.
We are given the following information:
q1 = -5.0
q2 = -15
F = 8.3×10^(-4)
Using Coulomb's law, we can rearrange the equation to solve for r:
r = √((k * (q1 * q2)) / F)
Now, let's substitute the given values:
r = √((k * (-5.0 * -15)) / 8.3×10^(-4))
The Coulomb's constant, k, is approximately equal to 8.99 × 10^9 N m^2/C^2.
r = √((8.99 × 10^9 * (-5.0 * -15)) / 8.3×10^(-4))
Simplifying,
r = √(134850 * 8.99 × 10^9 / 8.3×10^(-4))
r = √(1.201617 × 10^14 / 8.3×10^(-4))
r = √1.44890241 × 10^18
r ≈ 1.2 × 10^9 meters
Therefore, the distance between the spheres is approximately 1.2 × 10^9 meters.
To find the distance between the spheres, we can use Coulomb's Law:
F = k * (|q1| * |q2|) / r^2
Where:
F is the force of repulsion between the spheres (given as 8.3×10−4),
k is the Coulomb's constant (k = 8.988 × 10^9 N m^2 / C^2),
|q1| and |q2| are the magnitudes of the charges on the spheres (-5.0 C and -15 C, respectively),
and r is the distance between the spheres (what we need to find).
We can rearrange the formula to solve for r:
r = sqrt((k * (|q1| * |q2|)) / F)
Substituting the given values:
r = sqrt((8.988 × 10^9 N m^2 / C^2 * |-5.0 C| * |-15 C|) / (8.3×10−4 N))
Simplifying the expression:
r = sqrt((8.988 × 10^9 N m^2 / C^2 * 5.0 C * 15 C) / (8.3×10−4 N))
r = sqrt(30196.725 C^2 m^2 / N)
Calculating the square root:
r = 173.9 m
Therefore, the distance between the spheres is 173.9 meters.