Question

What is the magnitude of the charge difference?

3. Two insulating strings, each with length L = 0.80 m, hang from a common point. Attached to the other end of the strings are identical conducting spheres each with mass m = 0.0018 kg. Different quantities of charge are transferred to the spheres. As a result the spheres separate by a small distance x = 0.0070 m, note that . Using insulating instruments the spheres are forced together and are made to touch. The charge redistributes itself and subsequently the spheres separate by a different small distance x' = 0.0080 m. Initially, what is the magnitude of the charge difference? (Answer 0.91 nC)

Answer 1

- 1142 Coulomb's 4 e,r2 Law. Like charges repel Unlike charges attract 0 42

ー9x 109 N·m 2/C-Coulomb's constant k = _

let the angle initially is $\Theta$ = sin^-1(0.0035/0.8) = 0.25

and charges q and Q

forces on each point charges are :

mg downwards

electrical force Fe, left for the left charge and right for the right charge

tension T in the string

so at equilibrium

mg = T cos$\Theta$

Fe = T sin$\Theta$

so Fe/mg = tan $\Theta$

kqQ/mgr²  = tan$\Theta$

kqQ/mg(0.007²) = 0.004375

qQ = 4.19*10^-19 .......(1)

final charge on each is (q+Q)/2

and the angle $\Theta$' = 0.286

k(q+Q)²/4mgr²  = tan$\Theta$

k(q+Q)²/mg = 0.005*4*0.008²

(q+Q)² = 25.01*10^-19

q = 15.18*10^-10 -Q ....(2)

from (1) and (2)

(15.18*10^-10 -Q)Q = 4.19*10^-19

Q² -15.18*10^-10Q +4.19*10^-19 =0

Q = 12.21*10^-10 or 3.7*10^-10 C

so q = 15.18*10^-10 -Q = 15.18*10^-10 - 12.21*10^-10 = 2.97*10^-10 C

so the difference Q-q = (12.21-2.97)*10^-10 = 9.24*10^-10C = 0.92 nC