Finals Prep

NO Ampere’s Law, Flux, Torque, Gauss’s Law

NO section 6-7 on Chapter 16, Only sections 1-5 Chapter 19

Chapter 16

No section 6 or 7, No Gauss’s Law

Notes

• Similar charges are repulsive

• Opposite charges are attractive

• Weight difference in protons vs electrons

  • protons: +10,000

  • Electrons: -10,000

• Electric charge is both consumed and quantized

• Two charges with one positive and one negative has a net charge of 0

• 1e=1.60×10^-19 C

  • Can only be a multiple of e, never a fraction or decimal must be a whole number

• Initially neutral becomes positive by loosing electrons

• Conductors vs Insulators electron

  • Insulators are unable to let electron movement

  • Conductors let electrons free to move

• Must have one object charged and one neutral for electric interaction

• Electric repulsion happens when they have the same charge

• Electric attraction happens when the have different charges

• Semi conductors depend on the environment (thermal, heat, etc.) combining both conductor and insulator

• Force between two points

  • $F=\frac{k\left|q1\Vert q2\right|}{r^2}$

• Coulomb’s law calculating electric field

  • $E=\frac{F}{q}=\frac{k\left|q\right|}{r^2}$

• The electric field goes from negative to positive

• The magnetic field goes from North to South

• Particle movement with the electric field

  • A positive charge always accelerates with the electric field, goes with it

  • A negative charge goes against the electric field resulting in deacceleration

• Units for electric field is E=N/C or V/m

Practice problems

1. $q=25 nC$

   $=25×10^-9$

   $=25\times10^{-}9\left(\frac{1}{1.60\cdot10^{-19}}\right)$

   A:

2. $N=10^{15}e$

   $=10^{15}(1.60\times10^{-19})$

   A:

3. There are two protons, one is 2,000 times heavier, what is the force felt by both protons?

   A: They feel the same force even thought the masses are different

4. The force between two small charges is F, the distance between them is r, and if r is increased 3 times as large what happens to F?

   $F=\frac{k\left|q1\Vert q2\right|}{r^2}$

   $r\to3r$

   $F_{new}=\frac{k\left|q1\Vert q2\right|}{q\cdot r^2}$

   $=\frac{F}{q}$

5. What is the commonality between Newton’s Law and Coulomb’s Law?

   $\frac{1}{r^2}$ inverse equivalent

6. What direction is +Q going?

7. How do you find the net electric field at point P?

8. 71

9. 72

10. magnet

11. ball

12. triangle

Chapter 17

Notes

• Rules?

• U vs V

  • V=potential=voltage=?

  • U= energy(jouels)=electric potential energy=?

  • Explain the relationship between U and V?

    • They are related but not the same

    • $\Delta V=\frac{\Delta U}{q}$

    • Curves of U vs V

• *Don’t use absolute value terms in this chapter in reference to U and V*

• U is a scaler

  • If it needs to be added together simply add

• The SI units are J/C

• Electron volt is a form of energy

• Capacitance affected by three things…

  • Increase area

  • Reduce separation

  • Add dielectric material

• Electric field between capacitance

  • $E=\frac{o^{-}}{F_0}$

• Capacitance (C) stays the same when $\Delta V$ or Q …

• $Q=C\Delta V$

  • Proportional equation

    • You double one side of the equation the other doubles as well

    • For example if $\Delta V\to2\Delta V\Rightarrow Q\to2Q$

• Distance between two plates

  • $V=Ed$

  • $E=\frac{\sigma}{E_0}$

• When talking about two plates and capacitance

  • $Q\varpropto C$

  • $C\not\propto Q$

• $C_{eq}$ will be smaller than the smallest individual capacitor when in series

• $C_{eq}$ will be ____________________________when in parallel

Practice problems

1. Calculate U.

   *Either going to be square or triangle*

2. What happens when we double $\Delta V$ how does it affect q?

   $Q=C\Delta V$

   $Q=C\left(2\Delta V\right)$

   $=2Q$

3. EV

4. E at point P? or Electric potential at P?

5. Find $\Delta V$ ? $C=2\mu F$ , $Q=1C$

   $\Delta V=\frac{Q}{C}=\frac{1}{2\cdot10^{-6}}$

   $A\to2A\Rightarrow C\to2C$

6. What is the capacitance when you’re given $N=10^{10}$ electrons and $\Delta V=9$ volts?

   $Q=C\Delta V$

   $C=\frac{Q}{\Delta V}=\frac{Ne}{\Delta V}=\frac{\left(10^{10}\right)1.60\cdot10^{-19}}{9}=1.78\cdot10^{-10}F$

Chapter 18

Notes

• Right hand rule

  *If negative do the opposite force*

  • Thumb = Force

  • Pointer = Velocity

  • 3 Fingers = Magnetic Force

• Right hand rule for a wire

  • Thumb = Current

  • 4 Fingers = Curl to form the magnetic field direction

• L2 = 10% more = 0.1 L1

• L2 = 10% less = 0.9 L1

• Current is measured in amps

  • $i=\frac{\Delta q}{\Delta t}$

  • $1Amp=1C/Sec$

  • $1e=1.60×10^-19 C$

  • $1C=6.25×10^-18 e$

• In an electrical circuit it is only able to happen in a closed path $\Delta V$

  • $i$ at any point is the same

  • $i=V_{drift}neA$

• Velocity

  • 2 types

    • Regular velocity: $10^6$ m/sec $\Rightarrow$ Not relevant to current

    • Drift velocity:$10^{-5}$ m/sec $\Rightarrow$ Relevant to current

    • $V_{drift}=\frac{i}{neA}$

    • The size of the wire is not proportional

• Comparing wires

  • $\frac{R_1}{R_2}=\frac{\frac{\rho_1L_1}{A_1}}{\frac{\rho_2L2}{A2}}$

  • Having the same = cancel

• When things are stretched we have a conservation of volume

• $L_{initial}A_{initial=}L_{final}A_{final}$

• Omh’s law

  • $V=iR$

  • $R=\frac{\Delta V}{\Delta}$

  • \displaylines{V\varpropto i}

  • Slope must be in a 45° angle along the x-axis

• Kharkov’s rule

  • Loop: Conservation of energy rule

    • Provided energy is the consumed energy

    • \displaylines{\Delta V=0}

    • \displaylines{q-ir-iR=0}

  • Junction: Conservation of electric charges

    • The electric charges that come in are the same amount coming out

    • \displaylines{i=i_1+i_2}

• Series Circuits

  • \displaylines{R=R_1+R_2+R_{3\ldots}}

  • Highest resistance

  • Electric potential is the same throughout

• Parallel Circuits

  • \displaylines{\frac{1}{R}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}\ldots\Rightarrow R_{eq}=\frac{1}{\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}}}

  • Lowest resistance

  • Electric potential is the same throughout

• Power

  • The amount of energy

  • Measured in watts=J/sec

  • Three equal statements: \displaylines{P=iV=i^2R=\frac{V^2}{R}}

Practice problems

1. Find A2 in terms of A1 when a wire is stretched.

   $A_1L_1R_1=R$ →$A_2L_2R_2=25R$

   $\frac{A_2L_2R_2}{A_1L_1R_1}=A_2=\frac{L_2R_2}{A_1L_1R_1}$

   $\frac{R_1}{R_2}=\frac{\frac{\rho L_1}{A_1}}{\frac{\rho L_2}{A_2}}=\frac{L_1A_2}{L_2A_1}$

   $R=\frac{\rho L}{A}$

   $\frac{R}{25R}=\frac{L_1A_2}{L_2A_1}\Rightarrow\frac{1}{25}=\frac{L_1A_1}{L_2A_1}\Rightarrow\frac{L_2}{L_1}$

   $\frac{A_2}{A_1}=\frac{1}{25}\frac{L_2}{L_1}$

   $V_1=V_2$

   $A_1L_1=A_2L_2$

   $\frac{L_2}{L_1}=\frac{A_1}{A_2}\Rightarrow\frac{A_2}{A_1}=\frac{1}{25}\frac{A_1}{A_2}\Rightarrow\frac{A_2}{A_1}$

   $\frac{\left(A_2^{}\right)^2}{\left(A_1\right)^2}=\frac{1}{25}\Rightarrow A_2\frac15A_1$

2. When the cross-section of the wire is unchanging then how can we increase the current in the wire?

   A: By increasing the drift velocity

3. What are the three factors affecting resistance?

   $R=\frac{\rho L}{A}$

   A:Resistivity in material, length, and the cross-sectional area

4. Ex 9 in slides

5. Ex10 in slides

Chapter 19

Only sections 1-5

Notes

• Magnetism depends on movement (in motion)

• Magnetic field needs current

• \displaylines{F=qVB=qVB\sin\theta}

  • F is always perpendicular to V and B

Practice problems

1. What does force align with in a