Question

Two equally charged, 3.33 g spheres are placed with 4.665 cm between their centers. When released, each begins to accelerate at 268.36 m/s2. What is the magnitude of the charge, in micro-Coulombs, on each sphere?

Answer 1

Given,

Mass of each sphere = m = 3.33g = 3.33 x 10^-3 kg

Distance between sphere = d = 4.665 cm = 4.665 x 10^2 cm

Acceleration = a = 268.36 m/s^2.

Force on the sphere is given by the below formula,

`\begin{gathered} F=K((q1)(q2))/(d^2) \\ Where, \\ F=Force \\ K=Constant=9*10^9(Nm^2)/(C^2) \\ q1=q2=q=Charge \\ d=Distance\text{ }between\text{ }spheres \end{gathered}`
`\begin{gathered} We\text{ }can\text{ }write\text{ }Force\text{ }as, \\ F=ma \\ Where, \\ m=mass \\ a=acceleration \\ So, \\ F=ma=K((q1)(q2))/(d^2)=K(q^2)/(d^2) \\ \therefore q=d\sqrt[\placeholder{⬚}]{(ma)/(K)}=4.665*10^(-2)*\sqrt[\placeholder{⬚}]{(3.33*10^(-3)*268.36)/(9*10^9)}=46.484*10^(-8)C \\ \end{gathered}`

Result:- So the charge on the each sphere is 46.484 x 10^-8 C.