# Wright State University Lake Campus/2018-9/Phy2410/Notes

Quizbank/University Physics Semester 2(tests) and maybe Quizbank/Electricity_and_Magnetism_(calculus_based) (?)

### Tue 28 Aug

#### Lab1: Mr Circuit inventory

Mr. Circuit inventory: Check off what's missing during daytime hours have Engineering replace (main office is waiting for you.) Report: What is (or what do you think is) each of the following:

2. wire
3. battery
4. resistor
5. diode
6. potentiometer
7. Transistor/SCR (Both have three leads).

Report is written, due at end of period. Can be very informal, but write good and clear (and honest) prose. If time permits, research the items on the internet, but write only what you understand. Include the symbol for each element

#### Tues 4 Sep 2018 T1 review

Almost finished with T1. Will finish during recitation

#### Lab2 PheT virtual ciruit

Abstract: This PhET virtual kit has an option for using wires with finite resistance, and voltage sources with internal resistance. Also,the battery "catches fire" if too much power is involved. We will use this to "verify" Ohm's law under conditions where it is not quite true.

Goal: To create a simple circuit, perhaps using lightbulbs and/or added impedances to create a situation where Ohm's law is a good approximation, but not so good that the graph of I versus V is not a perfect straight line. You will need to use either Excel or Matlab to make your graph.

V I R
9 1 9.00
10 1.11 9.01
11 1.22 9.02
12 1.33 9.02
13 1.44 9.03

### Tues 11 Sep Test 2 Flux

#### Lab

1. Calculating area of a circle using integration over dA
2. Gauss Law: Concentric spheres

#### Recitation

Gauss law non-uniform but symmetric sphere

### Tues 18 Sep: Test 2*

* I removed our questions pending today's lab:

#### Recitation

Projects for Wikiversity. Explain

• Double sum for PE (work) N charges. We will 4x4 square. W_11 W_12 (after defining them) Equation 7.3
• Example 7.5:
30 Watts * (1 J/s / 1W) {  (V^-1) /  (Q/J) } 12 volts


## Tu 25 Sep: Start Test 3

### P=IV=(dq/dt)V=e(dN/dt)V relates power, voltage and e−/sec

Easy way to do Example 7.4:

This is much easier if you know the equations: Later in the course, we will establish: ${\displaystyle U=qV}$ and ${\displaystyle Power={\tfrac {\Delta U}{\Delta t}}={\tfrac {\Delta q}{\Delta t}}V=IV=e{\tfrac {\Delta N}{\Delta t}}}$

### Calculating Work with the 1/r potential

${\displaystyle Work=\int {\vec {F}}\cdot d{\vec {\ell }}=q\int {\vec {E}}\cdot d{\vec {\ell }}=kqQ\int _{r1}^{r2}{\frac {d{\tilde {r}}}{{\tilde {r}}^{2}}}=qQk\left({\frac {1}{r_{1}}}-{\frac {1}{r_{2}}}\right)}$

### Visualizing field lines and equipotentials

But the best is [PhET

### Capacitors "add" in parallel and series opposite to resistors

${\displaystyle {\text{Series}}:\;{\tfrac {1}{C_{S}}}=\sum {\tfrac {1}{C_{i}}}.}$   ${\displaystyle {\text{ Parallel:}}\;C_{P}=\sum C_{i}.}$

### Lab

Force on plate of a charged capacitor (quiz question)

• Van Der Graff generator
• Recitation: The class "wrote a report" that applied Gauss' law to capacitor using a wonderful website sponsered by physics.lousville, which has a great quote they claim was put forth by an electric company:

## Th 27 Sep Capacitors

### What to study for on Test 3

In the example quizzes (d_cp 2.7 and 2.8 series)

2.7 examples:

• example 7.1: study?
• example 7.2: not in study guide
• example 7.3: not on test
• example 7.4: know
• example 7.5: know
• example 7.6:easy
• example 7.8:easy, but not on test
2.6

• Study Examples 8.6 and 8.7. Both are on test, but on 8.7 you only need to find the charge (do so by finding the total capacitance and using the given voltage.)

## Thur 15:28, 4 October 2018 (UTC)

1. Do you already know this?
2. A Mathematician's Lament for reference only
4. w:Mathematical beauty
5. Amazing things I have seen in the classroom
6. quality MIT lecture on circuits

## Test 5 is Tuesday 29 30 October

The important examples in QB/d cp2.11 are:  Prob 1:Example 11.1     Prob 2:Example 11.2     Prob 3:Example 11.2     Prob 4:Example 11.4     Prob 5:Example 11.5     Prob 6:Example 11.7     Prob 7:Example 11.8     Prob 8:Example 11.9     Prob 9:Example 11.10

The important examples in QB/d cp2.12 are:  Prob 1:12.2     Prob 2:Example 12.3     Prob 3:Example 12.3     Prob 4:Example 12.4     Prob 5:Example 12.5     Prob 6:Example 12.7     Prob 7:Example 12.6?     Prob 8:Example 12.8     Prob 9:Example 12.8     Prob 10:Example 12.9     Prob 11:Example 12.10

## Next

### From wikipedia:Euler's formula

We begin with ${\displaystyle e^{x}=1+x+{\frac {(x)^{2}}{2!}}+{\frac {(x)^{3}}{3!}}+{\frac {(x)^{4}}{4!}}+{\frac {(x)^{5}}{5!}}+{\frac {(x)^{6}}{6!}}+{\frac {(x)^{7}}{7!}}+{\frac {(x)^{8}}{8!}}+\cdots }$

## d

{\displaystyle {\begin{aligned}i^{0}&=1,&i^{1}&=i,&i^{2}&=-1,&i^{3}&=-i,\\i^{4}&=1,&i^{5}&=i,&i^{6}&=-1,&i^{7}&=-i\\&\vdots &&\vdots &&\vdots &&\vdots \end{aligned}}}

For real values of x we have:

{\displaystyle {\begin{aligned}e^{ix}&=1+ix+{\frac {(ix)^{2}}{2!}}+{\frac {(ix)^{3}}{3!}}+{\frac {(ix)^{4}}{4!}}+{\frac {(ix)^{5}}{5!}}+{\frac {(ix)^{6}}{6!}}+{\frac {(ix)^{7}}{7!}}+{\frac {(ix)^{8}}{8!}}+\cdots \\[8pt]&=1+ix-{\frac {x^{2}}{2!}}-{\frac {ix^{3}}{3!}}+{\frac {x^{4}}{4!}}+{\frac {ix^{5}}{5!}}-{\frac {x^{6}}{6!}}-{\frac {ix^{7}}{7!}}+{\frac {x^{8}}{8!}}+\cdots \\[8pt]&=\left(1-{\frac {x^{2}}{2!}}+{\frac {x^{4}}{4!}}-{\frac {x^{6}}{6!}}+{\frac {x^{8}}{8!}}-\cdots \right)+i\left(x-{\frac {x^{3}}{3!}}+{\frac {x^{5}}{5!}}-{\frac {x^{7}}{7!}}+\cdots \right)\\[8pt]&=\cos x+i\sin x.\end{aligned}}}

But how can we verify that these infinite series expansions are valid?

2. Take derivatives: The series all match at x=0: ${\displaystyle e^{0}=1=\cos 0,{\text{ and }}\sin(0)=0}$. Term by term it is easy to show that ${\displaystyle de^{x}/dx=e^{x}}$ and also that the sine and cosine expansions also work out. If a polynomial and a function match values at x=0 and if all their derivatives match, does that mean that the (infinite) polynomieal (i.e. expansion) EQUALS the function? Not always.
3. Go deep into the mathematical logic of the calculus of complex numbers (called "complex analysis")

## Lab report due Tuesday 20 November

Full explanation based on Ampere's Law, Faraday's Law. I don't think you need Gauss's Law.

## 15 Nov Ray Diagrams

### Final Exam Examples

#### 2.12

2/11 from Special:Permalink/1892310 to QB/d_cp2.12 | Equations

#### 2.13

1. Example 13.1 from OpenStax University Physics2: https://cnx.org/contents/eg-XcBxE@9.7:BTZF6vX4@2/131-Faradays-Law_1
2. Example 13.2 from OpenStax University Physics2: https://cnx.org/contents/eg-XcBxE@9.7:ZNcjduzK@4/132-Lenzs-Law_1
3. Example 13.3 from OpenStax University Physics2: https://cnx.org/contents/eg-XcBxE@9.7:ZNcjduzK@4/132-Lenzs-Law_1
4. Example 13.3 from OpenStax University Physics2: https://cnx.org/contents/eg-XcBxE@9.7:ZNcjduzK@4/132-Lenzs-Law_1
5. Example 13.5 from OpenStax University Physics2: https://cnx.org/contents/eg-XcBxE@9.7:UbKygyP4@2/133-Motional-Emf_1
6. Example 13.6 from OpenStax University Physics2: https://cnx.org/contents/eg-XcBxE@9.7:UbKygyP4@2/133-Motional-Emf_1
7. Example 13.7 from OpenStax University Physics2: https://cnx.org/contents/eg-XcBxE@9.7:F-UkvfQz@3/134-Induced-Electric-Fields_1
8. Example 13.8 from OpenStax University Physics2: https://cnx.org/contents/eg-XcBxE@9.7:F-UkvfQz@3/134-Induced-Electric-Fields_1
9. Example 13.8 from OpenStax University Physics2: https://cnx.org/contents/eg-XcBxE@9.7:F-UkvfQz@3/134-Induced-Electric-Fields_1

#### 2.14

1. Example 14.1 from OpenStax University Physics 2: https://cnx.org/contents/eg-XcBxE@9.7:H8S6dNUY@2/141-Mutual-Inductance_1
2. Example 14.2 OpenStax University Physics 2: https://cnx.org/contents/eg-XcBxE@9.7:9IPDyGBX@2/142-Self-Inductance-and-Induct_1
3. Example 14.6 from OpenStax University Physics 2: https://cnx.org/contents/eg-XcBxE@9.7:gPV9xl9u@2/143-Energy-in-a-Magnetic-Field_1
4. Example 14.4 from OpenStax University Physics 2: https://cnx.org/contents/eg-XcBxE@9.7:vsb1s41R@3/144-RL-Circuits_1
5. Example 14.5 from OpenStax University Physics 2: https://cnx.org/contents/eg-XcBxE@9.7:vsb1s41R@3/144-RL-Circuits_1
6. Example 14.6 from OpenStax University Physics 2: https://cnx.org/contents/eg-XcBxE@9.7:tIlYnK5w@2/145-Oscillations-in-an-LC-Circ_1

#### 2.15

1. Example 15.1 from OpenStax University Physics2: http://cnx.org/content/col12074/1.3_1
2. Example 15.1 from OpenStax University Physics2: http://cnx.org/content/col12074/1.3_1
3. Example 15.1 from OpenStax University Physics2: http://cnx.org/content/col12074/1.3_1
4. Example 15.2 from OpenStax University Physics2: https://cnx.org/contents/eg-XcBxE@14.10:JOs6racw@8/15-3-RLC-Series-Circuits-with-AC
5. Example 15.4 from OpenStax University Physics2: http://cnx.org/content/col12074/1.3_1
6. Example 15.5 from OpenStax University Physics2: http://cnx.org/content/col12074/1.3_1
7. Example 7.15 from OpenStax University Physics2: https://cnx.org/contents/eg-XcBxE@9.8:z70YwVma@4/156-Transformers_1