Question

Two identical tiny spheres of mass m =2g and charge q hang from a non-conducting strings, each of length L = 10cm. At equilibrium, each string makes and angle θ =50 with the vertical. Find the size of the charge on each spere.

Answer 1

q = 7.88μC

Step-by-step explanation:

In the diagram attached, you can visualize the situation. Separation distance between the 2 charges is:

D = 2*L*sin θ = 0.1532m

From a sum of forces on the X-axis:

`T*sin \theta = Fe`

And on the y-axis:

`T*cos \theta = m*g` Solving for T and replacing its value on the X-axis equation we get:

`m*g*tan \theta = Fe` Since
`Fe = (K*q^2)/(D^2)`

`m*g*tan \theta = (K*q^2)/(D^2)` Solving for q we get:

q = 7.88μC