# Physics 1028 Chapter Notes - Chapter 17: Mechanical Equilibrium, Electric Field

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Selection of Even–Numbered Problem Solutions

Chapter 17

P–17.2

Initially, there is no electrostatic force since sphere B doesn’t carry a charge. After connecting both spheres,

the mutual repulsion of the mobile positive charges on sphere A leads to a maximum charge separation, given

when qA = Q/2 and qB = Q/2.

At this point we make a less obvious assumption: We assume that the uniformity of the charge dis-

tribution on either sphere is not disturbed by the other sphere. This assumption is reasonably justified as long

as the sizes of the two spheres are small in comparison to their distance. When this assumption is valid, the

entire charge on either sphere behaves as if it were a point charge at the centre of the sphere. Note that we

would have to consider all the individual point charges on each sphere separately without this assumption.

Using Coulomb’s law we find for the magnitude of the force between the two spheres:

(1)

This is a repulsive force because both spheres are positive.

P–17.4

The electrons in the atomic shell of helium are electrically balanced by the two protons in the nucleus. Thus,

the total amount of negative charge is:

(2)

Note that there are also two neutrons in each helium nucleus. Free neutrons decay into an electron and a

proton with a half–life of 14 minutes. In the above calculation we neglected these additional electrons because

neutrons in a nucleus are stable.

## Document Summary

Initially, there is no electrostatic force since sphere b doesn"t carry a charge. After connecting both spheres, the mutual repulsion of the mobile positive charges on sphere a leads to a maximum charge separation, given when qa = q/2 and qb = q/2. At this point we make a less obvious assumption: we assume that the uniformity of the charge dis- tribution on either sphere is not disturbed by the other sphere. This assumption is reasonably justified as long as the sizes of the two spheres are small in comparison to their distance. When this assumption is valid, the entire charge on either sphere behaves as if it were a point charge at the centre of the sphere. Note that we would have to consider all the individual point charges on each sphere separately without this assumption. Using coulomb"s law we find for the magnitude of the force between the two spheres: (1)