Projects & Practices in Physics 184_notes:examples
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2021-08-01T22:15:22+00:00Projects & Practices in Physics
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Return to Larger Combinations of Resistors and Capacitors notes
The Wheatstone Bridge
Suppose you have the following circuit -- it is similar to a well known circuit called a Wheatstone bridge. Resistors are labeled 1 through 4 for convenience of reference, and the fifth element is a light bulb, which also has some resistance. If any current at all flows through the light bulb, it will glow. You know $R_1 = 150 \Omega$$R_2=60 \Omega$$R_3$$R_3=250 \Omega$$R_4$$R_3=500 \Omega$$\Delta V_{\text{ba…text/html2021-07-22T14:21:57+00:00schram45 (schram45@undisclosed.example.com)184_notes:examples:week4_charge_cylinder
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Example: Electric Field from a Cylindrical Shell of Charge
Note: Super Challenge Problem!! -- This is a beyond the scope of this class (so you won't be expected to solve this kind of problem), but it is a cool example of how to expand from lines to areas of charge if you are interested
$R$$L$$Q$$R$$P$$z$$z = 0$$z$$P$$z$$Q$$L$$R$$xy$$z$$$\vec{E}=\frac{1}{4\pi\epsilon_0}\frac{Qz}{(R^2+z^2)^{3/2}}\hat{z}$$$P$$\text{d}Q$$\text{d}Q$$\text{d}Q$$\vec{r}$$\text{d}\vec{E}$$P$$\text{d}Q$$\text{d}Q$$\text…text/html2021-07-22T09:56:13+00:00schram45 (schram45@undisclosed.example.com)184_notes:examples:week14_step_down_transformer - [Solution]
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Return to Changing Flux from an Alternating Current notes
Designing a Step-down Transformer
Recall the discussion on voltage transformers. We designed a step-up transformer in the notes, which is used to convert small voltages from a generator into high voltages, which get carried long distances to residential areas. High-voltage power lines are dangerous, though, because the potential difference between the power lines and the ground is so enormous. Before the lines enter a residential area, …text/html2021-07-22T09:51:37+00:00schram45 (schram45@undisclosed.example.com)184_notes:examples:week14_b_field_capacitor
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Return to Changing Electric Fields notes
Magnetic Field from a Charging Capacitor
Suppose you have a parallel plate capacitor that is charging with a current $I=3 \text{ A}$. The plates are circular, with radius $R=10 \text{ m}$ and a distance $d=1 \text{ cm}$ apart. What is the magnetic field in the plane parallel to but in between the plates?$R=10 \text{ m}$$d=1 \text{ cm}$$I=3 \text{ A}$$I$$$\vec{E} = \frac{Q/A}{\epsilon_0} \hat{x}$$$Q$$A$$\hat{x}$$$\int \vec{B}\bullet \text{d}\vec{l} = \mu…text/html2021-07-13T09:26:15+00:00schram45 (schram45@undisclosed.example.com)184_notes:examples:week14_changing_current_rectangle - [Solution]
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Return to Changing Magnetic Fields with Time notes
Changing Current Induces Voltage in Rectangular Loop
Suppose you have an increasing current through a long wire, $I(t) = I_0 \frac{t}{t_0}$. Next to this wire, there is a rectangular loop of width $w$ and height $h$. The side of the rectangle is aligned parallel to the wire so that the rectangle is a distance $d$$I(t) = I_0 \frac{t}{t_0}$$w$$h$$h$$d$$V_{ind}$$I_{ind}$$$B = \frac{\mu_0 I}{2 \pi r}$$$$\Phi_B = \int \vec{B} \bullet \text{d}\vec{A…text/html2021-07-13T08:33:45+00:00schram45 (schram45@undisclosed.example.com)184_notes:examples:week12_force_loop_magnetic_field - [Solution]
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Return to Magnetic Force on a Current Carrying Wire notes
Force on a Loop of Current in a Magnetic Field
Suppose you have a square loop (side length $L$) of current $I$ situated in a uniform magnetic field $\vec{B}$ so that the magnetic field is parallel to two sides of the loop. What is the magnetic force on the loop of current?$L$$B$$I$$$\left| \vec{F} \right|=IBL\sin\theta$$$\theta$\[
\left| \vec{F} \right| = \begin{cases}
IBL\sin \pi = 0 & \text{top} \\
…