Question

Two small spheres each of mass 10^-6 kg are suspended from a point by silk threads 50 cm long. tgey are equally charged and repel each other to a distance 20 cm apart. calculate cgarge on each

Answer 1

Two small sphere of mass , m =10⁻⁶ Kg are suspended from a point thread of 50cm long as shown in figure. They are equally charged and repel each other to a distance 20cm apart.
Let charge on each sphere is q and tension on string is T
Let thread inclined with vertical at an angle θ
Then, at equilibrium condition ,
Downward force = upward force
mg = Tcosθ
10⁻⁶ × 10 = 10⁻⁵ = Tcosθ ------(1)
Forward force = backward force
Coulombs force = Tsinθ
Kq²/(0.20)² = Tsinθ [ because distance between two sphere is 20cm = 0.2m ]
9 × 10⁹q²/0.04 = Tsinθ
2.25 × 10¹¹ q² = Tsinθ -------(2)

Dividing equation (1) from equation (2)
2.25 × 10¹¹q²/10⁻⁵ = tanθ

Now, tanθ = 10/√{50² - 10²} = 10/20√6 = 1/2√6 [ see figure]
q² = 10⁻¹⁶/{2√6 × 2.25} = 10⁻¹⁶/(2×2.449 × 2.25)
q² = 9.07 × 10⁻¹⁸
taking square root both sides,
q = 3 × 10⁻⁹C