Question

In deep space two spheres each of radius 3.50 m are connected by a 3.46 ✕ 10² m nonconducting cord. If a uniformly distributed charge of 31.5 mC resides on the surface of each sphere, calculate the tension in the cord________N

Answer 1

To calculate the tension in the cord connecting two charged spheres in deep space, we can use the concept of electrostatic force. The tension in the cord is equal to the electrostatic force between the spheres, which can be calculated using Coulomb's law.

Step-by-step explanation:

To calculate the tension in the cord connecting two spheres in deep space, we can use the concept of electrostatic force. The tension in the cord can be equated to the electrostatic force between the spheres. The electrostatic force between two spheres with charges Q1 and Q2, and a distance d between their centers, can be calculated using Coulomb's law as:

Tension = (k * Q1 * Q2) / d²

In this case, the charges on each sphere are given as 31.5 mC. The value of k, the electrostatic constant, is approximately 9 × 10^9 N·m²/C². The distance between the centers of the spheres is given as 3.46 × 10² m. Substituting the values into the equation:

Tension = (9 × 10^9 N·m²/C² * 31.5 × 10^-3 C * 31.5 × 10^-3 C) / (3.46 × 10² m)²

Tension ≈ 2.954 N.