Question

two small spheres each having mass of 0.1 g are suspended from a point by threads 20 cm long. they are equally charged and they repel each other to a distance of 24 cm. what is the charge on each sphere​

Answer 1

Given info : Two small spheres each having mass of 0.1 g are suspended from a point by threads 20 cm long. they are equally charged and they repel each other to a distance of 24 cm.

To find : The charge on each sphere is ...

solution : see figure,

cosθ = 16/20 = 4/5

so, sinθ = 3/5 , where θ is angle made by thread with vertical line as shown in figure.

let tension in the thread is T,

at equilibrium,

Tcosθ = mg and Tsinθ = Fe = kq²/r²

⇒T × 4/5 = mg

⇒T = 5mg/4 ...(1)

and Tsinθ = Fe = kq²/r²

⇒T × 3/5 = kq²/r²

⇒T = 5kq²/3r² ....(2)

from equations (1) and (2) we get,

5mg/4 = 5kq²/3r²

⇒3mg/4 = kq²/r²

here m = 0.1 g = 10¯⁴ kg , g = 10 m/s², k = 9 × 10^9 Nm²/C², r = 24 cm = 0.24 cm

so, 3 × 10¯⁴ × 10/4 = (9 × 10^9) × q²/(0.24)²

⇒0.0576 × 10¯¹²/( 4 × 3) = q²

⇒q = 0.24 × 10¯⁶/(2 × √3) = 0.0693 × 10¯⁶ C

= 6.93 × 10^-8 C

Therefore charge on each sphere is 6.93 × 10^-8 C (approx)