Projects & Practices in Physics 184_notes http://msuperl.org/wikis/pcubed/ 2021-06-23T23:33:58+00:00 Projects & Practices in Physics http://msuperl.org/wikis/pcubed/ http://msuperl.org/wikis/pcubed/lib/tpl/bootstrap3/images/favicon.ico text/html 2021-06-21T14:22:38+00:00 schram45 (schram45@undisclosed.example.com) 184_notes:examples:week8_cap_series http://msuperl.org/wikis/pcubed/doku.php?id=184_notes:examples:week8_cap_series&rev=1624299758&do=diff Return to capacitors in series notes Example: Capacitors in Series Suppose you have the following circuit. Capacitors are labeled 1 and 2 for convenience of reference. You know that the circuit contains a 12-Volt battery, $Q_1=4.5 \mu\text{C}$, and $C_2=0.5 \mu\text{F}$. What is the capacitance of Capacitor 1? What happens to the charge on $k = 3$$\Delta V_{\text{bat}} = 12\text{ V}$$Q_1 = 4.5 \mu\text{C}$$C_2 = 0.5 \mu\text{F}$$k = 3$$C_1$$$C=\frac{Q}{\Delta V}\frac{1}{C_{\text{equiv}}}=\… text/html 2021-06-17T12:28:34+00:00 bartonmo (bartonmo@undisclosed.example.com) 184_notes:ind_i http://msuperl.org/wikis/pcubed/doku.php?id=184_notes:ind_i&rev=1623947314&do=diff Sections 22.1-22.3 in Matter and Interactions (4th edition) The Curly Electric Field and Induced Current Now that we have talked about the changing magnetic flux part of Faraday's law, we should go back to the right hand side and talk about the curly electric field (the $\int \vec{E}_{nc} \bullet d\vec{l}$$\vec{E}$$\vec{E}_{nc}$$V_{ind}$$V_{ind}$$\int \vec{E}_{nc} \bullet d\vec{l}$$\frac{V}{m}\cdot m= V$$V_{ind}=\int \vec{E}_{nc} \bullet d\vec{l}$$$\int \vec{E}_{c} \bullet d\vec{l}$$V_{ind}=… text/html 2021-06-17T12:08:41+00:00 bartonmo (bartonmo@undisclosed.example.com) 184_notes:b_flux http://msuperl.org/wikis/pcubed/doku.php?id=184_notes:b_flux&rev=1623946121&do=diff Section 22.2 in Matter and Interactions (4th edition) Changing Magnetic Flux In these notes, we will start thinking the right hand side of Faraday's Law (the \frac{d\Phi_{B}}{dt} part) and what it means to have a changing magnetic flux. Let's start by defining what flux is.$$\Phi_{B}= \vec{B} \bullet \vec{A}$$\Phi_{B}$$T \cdot m^2$$\vec{B}$$\vec{A}$$+y$$-y$$\vec{B}$$\vec{A}$$\Phi_{B}= |\vec{B}| |\vec{A}| cos(\theta)$$$\theta$$cos(\theta)=1$$cos(90) = 0$$\Phi_B = \int \vec{B} \bullet d\ve… text/html 2021-06-17T11:24:22+00:00 bartonmo (bartonmo@undisclosed.example.com) 184_notes:what_happens http://msuperl.org/wikis/pcubed/doku.php?id=184_notes:what_happens&rev=1623943462&do=diff Section 22.1 and 22.2 in Matter and Interactions (4th edition) What happens when Magnetic Fields Change? Thus far in this course, we have considered the electric and magnetic fields completely separately, either only looking at the effects of an electric field by itself or a magnetic field by itself. However, there are many real-world contexts where a charge may be moving in a magnetic field and also near other charges. This means the charge would feel both an \vec{F}_{net}=\vec{F}_1+\vec{F}_… text/html 2021-06-16T18:36:41+00:00 bartonmo (bartonmo@undisclosed.example.com) 184_notes:e_b_summary http://msuperl.org/wikis/pcubed/doku.php?id=184_notes:e_b_summary&rev=1623883001&do=diff Summary of Electricity and Magnetism (thus far) So far in this course we have primarily talked about static electric fields (Weeks 1 - 3), how static electric fields apply to circuits (Weeks 4 - 6), and static magnetic fields (Weeks 7 - 9). We have primarily been treating these phenomena as independent (i.e. only looking at the electric field or only looking at the magnetic field). However, as you may have guessed, these ideas are not completely separate. For example, let's say that you had a p… text/html 2021-06-16T18:14:07+00:00 bartonmo (bartonmo@undisclosed.example.com) 184_notes:b_summary http://msuperl.org/wikis/pcubed/doku.php?id=184_notes:b_summary&rev=1623881647&do=diff Summary of Magnetic Fields and Force It is an experimental fact that moving electric charges generate magnetic fields in all of space. When we observe a magnetic field, we know that is often due to some charge or collection of charges that are moving relative to our location in space (unless it’s due to a changing electric field as we will see soon).$$\vec{B} = \dfrac{\mu_0}{4\pi} \dfrac{q \vec{v} \times \hat{r}}{r^2}\vec{B} = \dfrac{\mu_0}{4 \pi} \int \dfrac{I d\vec{l} \times \hat{r}}{r^2… text/html 2021-06-16T18:02:34+00:00 bartonmo (bartonmo@undisclosed.example.com) 184_notes:i_b_force - [Force on a little chunk] http://msuperl.org/wikis/pcubed/doku.php?id=184_notes:i_b_force&rev=1623880954&do=diff Section 20.2 in Matter and Interactions (4th edition) Magnetic Force on a Current Carrying Wire Since we deal with currents on a daily basis in all of electronics, it is particularly important and relevant to consider the force on a current-carrying wire. These notes will step through how get from the magnetic force on a single moving charge to the force on a current. $$d\vec{F}= dq \vec{v}\times\vec{B}$$$dq$$\vec{v}$$\frac{m}{s}$$\vec{B}$$T$$\vec{v}=\frac{d\vec{l}}{dt}$$$d\vec{F}= dq \frac{d… text/html 2021-06-16T15:24:30+00:00 bartonmo (bartonmo@undisclosed.example.com) 184_notes:b_shapes http://msuperl.org/wikis/pcubed/doku.php?id=184_notes:b_shapes&rev=1623871470&do=diff Shapes of Wires and Magnetic Fields Thus far, we have primarily been talking about the magnetic field from a current in a long, straight wire. However, there are many shapes of wire in the real world that do not correspond to straight wires. Particularly relevant to this class will be a coil of wire and something we will call a solenoid. These notes go more into detail about what coils and solenoids are, and what the magnetic field looks like from both coils and solenoids.$dl$$\vec{B}_{tot}= \… text/html 2021-06-16T15:16:22+00:00 bartonmo (bartonmo@undisclosed.example.com) 184_notes:b_sup_comp http://msuperl.org/wikis/pcubed/doku.php?id=184_notes:b_sup_comp&rev=1623870982&do=diff Using Superposition of Magnetic Field and the Computer In the previous page of notes, we talked about how you can use superposition to calculate the magnetic field from a current rather than thinking about each individual moving charge. We ended up with an equation for the magnetic field where$$\vec{B}_{tot}= \int \frac{\mu_0}{4 \pi}\frac{I \cdot d\vec{l}\times \hat{r}}{r^2}$$I$$d\vec{l}$$\vec{r}$$$\vec{B}_{net} = \sum \vec{B}_i = \vec{B}_1 + \vec{B}_2 + \vec{B}_3 + \dots$$\vec{B}_1$$\vec{B}_… text/html 2021-06-16T15:04:28+00:00 bartonmo (bartonmo@undisclosed.example.com) 184_notes:b_current http://msuperl.org/wikis/pcubed/doku.php?id=184_notes:b_current&rev=1623870268&do=diff Sections 17.2 and 17.6-17.8 in Matter and Interactions (4th edition) Currents Make Magnetic Fields Now that we have talked about a single moving charge and permanent magnets, the next source of magnetic fields that we are going to consider is currents (either comprised of electrons or some other charged particle). This builds on what we learned about$\$\vec{B}_{tot}=\frac{\mu_0}{4 \pi}\frac{q_1\vec{v}\times \hat{r_1}}{r_1^2}+\frac{\mu_0}{4 \pi}\frac{q_2\vec{v}\times \hat{r_2}}{r_2^2}+\frac{\mu… text/html 2021-06-16T14:50:11+00:00 bartonmo (bartonmo@undisclosed.example.com) 184_notes:perm_mag http://msuperl.org/wikis/pcubed/doku.php?id=184_notes:perm_mag&rev=1623869411&do=diff Section 17.11 and 17.12 in Matter and Interactions (4th edition) Permanent Magnets In addition to moving charges, another source of magnetic fields that we are going to talk about are permanent magnets. These are the magnets that probably you have seen, have experience with, and already know about (i.e. refrigerator magnets, the Earth, the traditional U-shaped magnets, etc.). While these are much more frequently used in everyday life, permanent magnets are actually quite complicated and are an…