Question

Two equally charged spheres of mass 1.0 g are placed 2.0 cm apart. When released, they begin to accelerate at 980 m/s2. What is the magnitude of the charge on each sphere? Two equally charged spheres of mass 1.0 g are placed 2.0 cm apart. When released, they begin to accelerate at 980 m/s2. What is the magnitude of the charge on each sphere? 210 nC 120 nC 180 nC 150 nC

Answer 1

210nC

Step-by-step explanation:

The force experimented by two charges
`q_1` and
`q_2` separated a distance
`r` is given by Coulomb's Law:

`F=(kq_1q_2)/(r^2)`

where
`k=9*10^9Nm^2/C^2` is the Coulomb constant.

The acceleration experimented by any (both) of them will be given by Newton's 2nd Law: F=ma

Combining both equations and considering that
`q_1=q_2=q`, we get:

`ma=(kq^2)/(r^2)`

Which means:

`q=\sqrt{(mar^2)/(k)}`

Which for our values is:

`q=\sqrt{((0.001kg)(980m/s^2)(0.02m)^2)/(9*10^9Nm^2/C^2)}=2.09*10^(-7)C=209*10^(-9)C=209nC`

Which is very close to the option 210nC