Question

A large positively-charged object with charge q_+ = 4.25 mu C is brought near a negatively-charged plastic ball suspended from a string of negligible mass. The suspended ball has a charge of q_- = -54.3 nC and a mass of 16.5 grams. What is the angle the string makes with the vertical when the positively charged object is 22.5 cm from the suspended ball? The positively-charged object is at the same height as the suspended ball.

Answer 1

From the diagram

Force between the charged objects is given as

F = k q₁ q₂/r² =(9 x 10⁹) (54.3 x 10^-9) (4.25 x 10^-6) / (0.225)² = 0.041 N

Along Y-direction, force equation is given as

T Cos$\theta$ = mg                              eq-1

Along X-direction, force equation is given as

T Sin$\theta$ = F                              eq-2

Dividing eq-2 by eq-1

tan$\theta$ = F/mg

tan$\theta$ = 0.041 / (0.0165x 9.8)

$\theta$ = 14.25