(c) Explain what happens to the balls if one of them is suddenly discharged (by
ID: 2004323 • Letter: #
Question
(c) Explain what happens to the balls if one of them is
suddenly discharged (by whatever means). Think: these are
conducting spheres—what happens if they touch?
(d) Find the new equilibrium separation x, using the given
values of L and m and the computed value of | q |.
two tiny conducting balls of identical mass m and identical charge +q hang from non-conducting threads of length L. Assume that the half-separation angle theta is so small that tan theta can be replaced by its approximate equal, sin theta. (a) Show the equilibrium separation x of the balls is given by x=(q^2L/2piepsilon0mg)^1/3 (b) If L = 120 cm, m = 10 gm, and x = 5.0 cm, what is | q |? (c) Explain what happens to the balls if one of them is suddenly discharged (by whatever means). Think: these are conducting spheres?what happens if they touch? (d) Find the new equilibrium separation x, using the given values of L and m and the computed value of |q|.Explanation / Answer
the mass of the sphere = m,the charge of the each sphere = q (a) There are three forces acting on each sphere:
1) The tension T of the string
2) The weight W of the sphere (Y axis direction)
3) The force Fe of electrostatic repulsion (X axis direction)
From the equilibrium equations:
Fx = T sin – Fe = 0 ------------- (1)
Fy = T cos – W = 0 ---------------(2)
where T = string tension
Fe = k * q ² / X ² = Coulomb’s force (N)
W = M * g = weight of each sphere (N)
X = distance between charges (m)
From (1)
T = Fe / sin ---------------- (3)
Replacing in (2)
Fe = W * tan = M * g * tan --------- (4)
From Coulomb’s law
Fe = k * q² / X² ------------ (5)
From (4)& (5)
M * g * tan = k * q² / X² -------- (6)
The length L of the string is
L = X / (2 * sin ) ---------------------(7)
From (6) & (7)
X = (q^2*KL2/mg)^1/3
X = (q^2L/2mg)^1/3
------------------------------------
(b) if L = 120*10^-2 m , X = 5.0*10^-2 m , m = 10*10^-3 kg
q^2 =mg* x^3/2kL
= 10*10^-3*9.8*(5.0*10^-2)^3/2*9*10^9*120*10^-2
q =2.38*10^-8 C
(c) when the two spheres are in contact, this charge shared by two spheres.
the new charge in an each sphere, q ' = 2.38/2*10^-8 C
q' = 1.19 *10^-8 C
(d) the new x' = (q^2*KL2/mg)^1/3
= 1.417*10^-16*9*10^9*120*10^-2*2/10*10^-3*9.8
= 3.14*10^-2 m
or x' = 3.14 cm
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