Question

The force between a positively charged foam cup and a positively charged metal sphere is 5.2 × 10^−4 newtons. The charge on the cup is 7.2 × 10^−6 coulombs, and the charge on the metal sphere is 6.8 × 10^−6 coulombs. What is the distance between the two objects? (k = 9.0 × 10^9 newton·meters^2/coulombs^2)

A) 0.2 meters
B) 0.4 meters
C) 0.6 meters
D) 0.8 meters

Answer 1

To find the distance between two charged objects, we can use Coulomb's law. By plugging in the given values into the equation and solving for r, we find that the distance between the objects is approximately 9.41 meters.

Step-by-step explanation:

To find the distance between the two objects, we can use Coulomb's law, which states that the force between charged objects is 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 force, k is the electrostatic constant, q1 and q2 are the charges, and r is the distance between the objects.

Plugging in the given values:

F = 5.2e-4 N, q1 = 7.2e-6 C, q2 = 6.8e-6 C, and k = 9.0e9 N*m^2/C^2.

Plugging these values into the equation and solving for r:

r^2 = (k*q1*q2)/F

r^2 = (9.0e9 N*m^2/C^2)*(7.2e-6 C)*(6.8e-6 C)/(5.2e-4 N)

r^2 = 88.615 m^2

r = sqrt(88.615) m

r ≈ 9.41 m

Therefore, the distance between the two objects is approximately 9.41 meters.