electrostatics – Worksheet 1 problem solution (Q2)

Question 2) In the picture below, X is a small negatively charged sphere with a mass of 10kg. It is suspended from the roof by an insulating rope which makes an angle of 60o with the roof. Y is a small positively charged sphere that has the same magnitude of charge as X. Y is fixed to the wall by means of an insulating bracket.

Assuming the system is in equilibrium, what is the magnitude of the charge on X?

figure: Q2 supporting diagram

[ here is the complete worksheet: electrostatics worksheet 1 ]

Solution:

determining the charge on X – to determine their charges it’s required to know the force between X and Y & we can use Coulomb’s Law as we know the distance between them.

So, firstly, we need to determine the magnitude of the electrostatic force between X and Y.

The distance between X and Y is 50cm = 0.5m, and the mass of X is 10kg.

Draw the forces on X (with directions) and label.

Determine the magnitude of the electrostatic force (FE). Since nothing is moving (the system is in equilibrium) the vertical and horizontal components of the forces must cancel. Thus:

The only force we know is the gravitational force Fg = mg. Now we can calculate the magnitude of T from above:

This means that FE is:

Now that we know the magnitude of the electrostatic force between X and Y, we can calculate their charges using Coulomb’s Law. Don’t forget that the magnitudes of the charges on X and Y are the same: |QX| = |QY|. The magnitude of the electrostatic force is:

Thus the charge on X is -1.27 x 10-4 C

[ here is the complete worksheet: electrostatics worksheet 1 ]

electrostatics – Worksheet 1 problem solution (Q2)
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