PHL232H1 Lecture Notes - Lecture 3: If And Only If

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Wednesday, October 5, 2016

PHL232 Tutorial Notes

Counterfactuals and Nozick

S-L Semantics: Is a semantics about the counterfactual

p counterfactual q”: If it would be the case that p it would be the case that q is true at a

world where iff: There is a world x in which p^q is true that is closer to the w than any

world y in which p^notq is true.

@is used as a symbol for the actual world.

There is a world x in which p^q is true that is closer to @ than any world y in which

p^notq is true.

Closer means more similar. Is this similarity based on some objective feature? Yes. S-L

say that similarity is an objective feature that worlds have. This needs to be objective for

the account not to be circular.

Nozick

Nozicks theory on what consitutes knowledge (4 conditions)—Nozicks account does

not relate to the sceptic on their terms but is supposed to explain to those of us who are

not sceptics how to determine what knowledge is.

1. It is true that P

2. I believe that P

3. Subjunctive: If P wasnt true then I wouldnt believe P.

1. There is a world in which I dont believe P and P is not true, that is closer then

any world in which P isnt true but I believe P.

4. If P is true then I would believe P.

1. Do I know that I have hands?

1. It is true that I have hands

2. I believe that I have hands

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Document Summary

@is used as a symbol for the actual world. There is a world x in which p^q is true that is closer to @ than any world y in which p^notq is true. S-l say that similarity is an objective feature that worlds have. This needs to be objective for the account not to be circular. Wednesday, october 5, 2016: if i didn(cid:1685)t have hands then i wouldn"t believe that i did. > there is a world in which i have hands and believe that i do that is closer than any world in which i have hands but i don(cid:1685)t believe that i do. **remember that we are looking at a world that is distinct from the actual world. The last proposition is true because the world in which i do and i believe that i do is closest to the actual world.

Related Questions

For a finite continuous charged object we can use integration tofind the electric potential at a point. As is the case for anyfinite charge distribution, the value of the electric potential canbe chosen to be zero at any reference point which is sufficientlyfar from the distribution. I.e. One can (and usually does) chooseV_(infinity) = 0 at r = infinity.

Consider a rod of length L extending from the origin along thepositive x axis, and a point P located at x = -D, which is adistance D from the origin. The task is to find the electricpotential (voltage) at the point P.

ChargedRod

The above Figure shows the rod. Highlighted is one small piece ofthe rod which is located at a position x and has length (dx). Note:In answers below, if you want to include dx, it is good practice toput (dx) in parentheses.

(a) Suppose that the rod is uniformly charged to a value Q. Writethe expression for the linear charge density, using the symbolsalready defined.
lambda = 1Click here to preview your answer.

(b) The small piece of the rod has length dx. In terms of symbolsL, x, (dx), D, Q and constants, what is the infinitesimal charge onthe rod? You may need to enclose dx in parentheses for it todisplay properly.
dq = 2Click here to preview your answer.

c) What is the distance from the point to the small piece of therod? Answer in terms of symbols x, L, D, (dx) and constants.
3Click here to preview your answer.

(d) What is the infinitesimal voltage produced at point P from thisdq? Answer in terms of symbols k, Q, x, L, D, (dx) andconstants.
dV = 4Click here to preview your answer.

(e) The final step would be to integrate this result. What are thelower 5Click here to preview your answer.
and upper 6Click here to preview your answer. limits on theintegration? Answer in terms of symbols x, L, D, (dx) andconstants.

Note that if the charge of the rod had not been uniform, we wouldneed to know lambda as a function of x and use that in place of(Q/L).

One facet of the central field approximation for many-electronatoms is that inner-shell electrons screen the nuclear charge. Tounderstand how this works quantitatively, first note that theprobability distributions for electrons in different shellsgenerally do not overlap much. For instance, the electrons in the Mshell (n=3) are almost always farther from the nucleus than theelectrons of the K (n=1) and L (n=2) shells. Thus, it is a goodapproximation to assume that the inner shells completely screen thenucleus from the outer shells. For example, if there are tenelectrons altogether in the K and L shells of an atom, then theelectrons in the M shell experience force from a charge of roughlyZ-10, where Z is the charge on the nucleus as an integer multipleof e, the magnitude of the charge on an electron. This is calledthe effective nuclear charge Z_eff.

a. In a beryllium atom (Z=4), how many electrons are in the Kshell?
Express your answer as an integer.

b. n xenon (Z=54), what is the effective charge Z_eff experiencedby an electron in the M (n=3) shell?
Express your answer as an integer.

c. How many electrons are there altogether in the K, L, and Mshells of xenon? Recall that for n=3, the orbital quantum number lmust be zero, one, or two and that m_l can take any value betweenpostive and negative l.
Express your answer as an integer.

d.

The idea of simply subtracting the number of inner-shell electronsworks well only for atoms with low values of Z. For atoms withlarger nuclear charge, the different shapes of the probabilitydistributions for different subshells becomes an important factor.For instance, in the N shell, electrons in the s subshell have amuch higher probability than those in the p or d subshells of beingfound closer to the nucleus than some of the K, L, or M electrons.It is said that the s electrons penetrate the inner shells morereadily than do the p or d electrons. Therefore, it is to beexpected that our simple subtraction model may not work well forouter-shell s electrons in large atoms. Keeping this in mind, wesee that the effective nuclear charge Z_eff for the outermostelectron in an atom may be found experimentally by measuring theionization energy of an atom and then calculating the effectivecharge using the equation

E_n=- \frac{Z_{\rm eff}^2}{n^2}(13.6\;\rm eV).

The energy for the 5p valence electron in indium (Z=49) is -5.79electron volts. What is the effective nuclear charge Z_effexperienced by this electron?
Express your answer to three significant figures.

1.Two uncharged, conducting spheres, A and B, are held at rest oninsulating stands and are in contact. A positively charged rod isbrought near sphere A. While the rod is in place, the two spheresare separated. How will the spheres be charged, if at all, afterthey are separated?
Sphere A Sphere B
(a) positive positive
(b) positive negative
(c) negative positive
(d) negative negative
(e) zero zero

2. A charged conductor is brought near an uncharged insulator.Which one of the following statements is true?
(a) Both objects will repel each other.
(b) Both objects will attract each other.
(c) Neither object exerts an electrical force on the other.
(d) The objects will repel each other only if the conductor has anegative charge.
(e) The objects will attract each other only if the conductor has apositive charge.

3. An electron is moved from point A, where the electric potentialis VA = â240 V, to point B, where the electric potential is VB =â360 V. What is the change in the electric
potential energy?
(a) 1.92Ã10â17 J (b) 2.04Ã10â17 J (c) 5.75Ã10â17 J (d) 8.98Ã10â17 J(e) 1.05Ã10â16 J

4. A -2q charge is located a distance d to the right of a +4qcharge, along the x
axis. At which point (or points) along the axis does the electricfield go to zero? To
solve this problem, consider an observer at point P, which is anarbitrary distance x from the +4q charge. Find the value (orvalues) for x (in terms of the separation distance d) where thetotal electric field vanishes.
(a) The electric field is never zero in the vicinity of thesecharges.
(b) The electric field is zero at x = -0.328d.
(c) The electric field is zero at x = +4.22d.
(d) The electric field is zero at both x = -2.26d and x =+2.26d.
(e) The electric field is zero at x = +3.41d.

5. point A is a distance L away from a point charge Q. Point B is adistance 4L away from Q. What is the ratio of the electrostaticpotential at B to that at A, i.e., what is VB/VA?
(a) 1/16
(b) 1/9
(c) 1/4
(d) 1/3
(e) can not be determined without specifying Q and L

6. Which one of the following statements best explains why it ispossible to define an electric potential
in a region of space that contains an electric field?
(a) Work must be done to bring two positive charges closertogether.
(b) Like charges repel one another and unlike charges attract oneanother.
(c) A positive charge will gain kinetic energy as it approaches anegative charge.
(d) The work required to bring two charges together is independentof the path taken.
(e) A negative charge will gain kinetic energy as it moves awayfrom another negative charge.

PHL232H1 Lecture Notes - Lecture 3: If And Only If

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