Question

A small plastic sphere with a charge of -6.0 nC is near another small plastic sphere with a charge of -14 nC . If the spheres repel one another with a force of magnitude 8.3×10−4 N , what is the distance between the spheres?

Answer 1

To find the distance between the two plastic spheres, we can use Coulomb's law. We have the force, charges, and the constant k. By rearranging the equation and substituting values, we find that the distance is approximately 0.068 meters.

Step-by-step explanation:

To solve this problem, we can use Coulomb's law, which states that the 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.

Let's assume that the distance between the spheres is d meters.

According to Coulomb's law, we have the equation:

Force = k * (|q1| * |q2|)/d^2

where k is a constant and represents the electrostatic force constant.

In this case, we have:

8.3×10−4 N = k * (|-6.0 nC| * |-14 nC|)/d^2

Since both charges are negative and have the same sign, we can write the equation as:

8.3×10−4 N = k * (6.0 nC * 14 nC)/d^2

Simplifying the expression and substituting values, we get:

8.3×10−4 N = k * 84 nC^2/d^2

To find d, we need to determine the value of k. k is equal to 9 x 10^9 N m^2/C^2, which is a constant. Substituting this value, we can solve for d by rearranging the equation:

d = sqrt((k * 84 nC^2)/8.3×10−4 N)

Calculating this, we find that the distance between the spheres is approximately 0.068 meters.

Answer 2

Here is how to answer the question.

Use the formula:
F = kq1q2/r^2

F = force = 8.3x10^-4N
q1, q2 = charges
r = separatioon
k = constant = 9x10^9 in MKS units

so we have

r = sqrt[k q1 q2/F]
r = sqrt[9x10^9*(-14)x10^-9 * (-6)x10^-9 / 8.3x10^-4 ]
r = 0.0302 m

So the distance between spheres is 0.0302 m