# resolução

(Parte 3 de 11)

where R is the radius of the soda can.

Because the empty can is a hollow cylinder: 2MRI= where M is the mass of the can.

Substitute for I and α and solve for

Substitute for F in equation (1):

Chapter 21 10

nC141

24 •• Picture the Problem Because the nucleus is in equilibrium, the binding force must be equal to the electrostatic force of repulsion between the protons.

Apply 0=∑Fr to a proton:

Solve for Fbinding: ticelectrostabinding F =

Using Coulomb’s law, substitute for

Felectrostatic:

kqF=

Substitute numerical values and evaluate Felectrostatic:

Electric Charge

25 • Picture the Problem The charge acquired by the plastic rod is an integral number of electronic charges, i.e., q = ne(−e).

Relate the charge acquired by the plastic rod to the number of electrons transferred from the wool shirt:

Solve for and evaluate ne: 12

Picture the Problem One faraday = NAe. We can use this definition to find the number of coulombs in a faraday.

Use the definition of a faraday to calculate the number of coulombs in a faraday:

The Electric Field 1: Discrete Charge Distributions 1

*27 • Picture the Problem We can find the number of coulombs of positive charge there are in

1 kg of carbon from, where nenQC6=C is the number of atoms in 1 kg of carbon and the factor of 6 is present to account for the presence of 6 protons in each atom. We can find the number of atoms in 1kg of carbon by setting up a proportion relating Avogadro’s number, the mass of carbon, and the molecular mass of carbon to nC.

Express the positive charge in terms of the electronic charge, the number of protons per atom, and the number of atoms in 1 kg of carbon:

enQC6=

Using a proportion, relate the number of atoms in 1 kg of carbon nC, to Avogadro’s number and the molecular mass M of carbon:

MmN n CA

M mNnCAC=

Substitute to obtain: M emNQCA6=

Substitute numerical values and evaluate Q:

Coulomb’s Law

28 • Picture the Problem We can find the forces the two charges exert on each by applying

1 to q2 is in the positive x direction.

(a) Use Coulomb’s law to express

the force that q1 exerts on q2:

Chapter 21 12

(b) Because these are action-andreaction forces, we can apply Newton’s 3rd law to obtain:

(c) If q2 is −6.0 µC:

We can find the net force on q1 by adding these forces.

Express the net force acting on q1:

Express the force that q2 exerts on

Express the force that q3 exerts on qqkr

Substitute and simplify to obtain:

i iiF ˆ

rqr q qk r qqkr qqkr

Substitute numerical values and evaluate 1Fr :

The Electric Field 1: Discrete Charge Distributions 13

30 •• Picture the Problem The configuration of the charges and the forces on the fourth charge are shown in the figure … as is a coordinate system. From the figure it is

evident that the net force on q4 is along the diagonal of the square and directed away from q3. We can apply Coulomb’s law to

and then add them to find the net force on q4.

Express the net force acting on q4:

(Parte 3 de 11)