Question

Two very small 8.80g spheres, 17.0cm apart from center to center, are charged by adding equal numbers of electrons to each of them.

Part A
-Disregarding all other forces, how many electrons would you have to add to each sphere so that the two spheres will accelerate at 23.0g when released?

N = ______________ electrons

Part B
-Which way will they accelerate?



Could somebody give a concise approach to this problem? Thank you.

Answer 1

Given that

mass of each sphere is m = 8.80x 10^-3 kg

acceleration due to gravity g =9.80 m/s2

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We have

      F = ma

But electrostatic force is

            F = kq^2/r^2

    kq^2/r^2 =  ma

Here r = 8.5x10^-2 m

So the charge on the sphere is

           q = √[mar^2/k]

              = √[(8.80x 10^-3 kg)(23(9.8 m/s2))(8.5x10^-2 m)^2/(9.0x10^9 N.m2/C2)]

              = 1.26x10^-6C

The number of electrons are

            n =q/e

               = (1.26x10^-6C)/(1.6 x10^-19 C)

               = 7.88x10^+12

b) two sphere are repul each other