An initially neutral conducting sphere is charged by induction. A second, identi

Question

An initially neutral conducting sphere is charged by induction. A second, identical, conducting sphere that is electrically neutral is brought into contact with the first and then removed. When the two spheres are placed next to each other such that their centers are a distance 5.0 cm apart, they exert a force of 0.002 N on each other. Determine the amount of charge that was placed on the first sphere by the induction process. Determine the amount of charge on each sphere after they are brought in contact. If an electron is placed between the two sphere's a distance 2.5 cm from the first (so that it is halfway between the two), what net force would be exerted on the electron? If an electron is placed between the two sphere's a distance 2.0 cm from the first (so that it is 3.0 cm from the second), what net force would be exerted on the electron?

Explanation / Answer

let charge on first sphere is Q.

after the second sphere is brought into cdontact with first one,
both the sphere will share the charge Q equally.

then charge on both the spheres=Q/2

force between them =9*10^9*(Q/2)*(Q/2)/0.05^2=0.002

==>Q=1.8856*10^(-5) C

part A:

charge placed on first sphere was 1.8856*10^(-5) C=18.856 uC

part B:

after they are brought in contact, charge on each sphere=Q/2=9.428 uC

part C:

both the spheres will exert same force and in opposite direction.

hence net force=0

part D:

charge on electron=q=-1.6*10^(-19) C

as distance is not equal, there will be a non-zero net force on electron.

net force=9*10^9*( ((Q/2)*q/0.02^2) - ((Q/2)*q/0.03^2))=1.8856*10^(-11) N

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