Question: Two small spheres, each having a mass of 20 g, are suspended from a common point by two insulating strings of length 40 cm each. The spheres are identically charged and the separation between the balls at equilibrium is found to be 4 cm. find the charge on each spheres.
What I have done:
Given, m = 20 g
distance between the balls = 0.04 m
length of strings = 0.4 m
After making a free body diagram, I got two equations.
Tcosθ = F (electrostatic force)
Tsinθ = mg
Dividing the two, tanθ = mg/F - (i)
Now, looking at the triangle made in the figure, I dropped a perpendicular from the vertex from where the two strings are joined.
Looking at the new right angled triangle, I found the length of the perpendicular. It comes out to be 0.3994.
So, tanθ = 0.3994/0.02 = 19.97
Now looking at the equation (i), I put the value of tanθ.
Therefore, F = mg/19.97.
I'm taking g = 10m/s²
F = 10(20)/19.97
F= 10.015
(9 x 10⁹ x Q²)/0.0016 = 10.015
Q² = 1.78 x 10⁻¹²
Q = 1.334 x 10⁻⁶
Well, that's what my answer comes, but it's wrong. Can someone guide me where I got it wrong?
