Question

Two small balls having equal positive charge Q on each are suspended by two insulating strings of equal length L from hook fixed to stand. What is the tension in the strings if whole set up is taken in a satellite?

Answer 1

In a satellite, where the setup is in a microgravity environment, the tension in the strings holding the charged balls can be determined by considering the electrostatic forces acting on the balls.

Let's assume the distance between the centers of the two charged balls is d. Since the charges on the balls are equal and positive, they will exert a repulsive electrostatic force on each other. This force can be calculated using Coulomb's law:

$F=\frac{k\cdot Q^2}{d^2}$

where F is the electrostatic force between the balls, Q is the charge on each ball, d is the distance between their centers, and k is the electrostatic constant.

Now, let's analyze the forces acting on each ball individually. Since the system is in a microgravity environment, the tension in the strings will provide the necessary centripetal force to keep the balls in circular motion. This centripetal force is given by:

$F_{\text{centripetal}}=\frac{m\cdot v^2}{r}$

where m is the mass of each ball, v is the velocity of the balls in their circular path, and r is the radius of their circular path.

In this case, we can assume the balls are in equilibrium, meaning the electrostatic force and the tension forces are balanced. Since the strings are of equal length L, the radius of the circular path can be taken as L.

Equating the centripetal force and the electrostatic force:

$\frac{m\cdot v^2}{L}=\frac{k\cdot Q^2}{d^2}$

Now, let's express v in terms of the radius and angular velocity ω:

v=ω⋅Lv = ω cdot Lv<span class="mspace" style="margin-right: 0.277