E & M: Review Part San

VERSION # 1.51

Last Updated 5:48 PM 2/22/2019

#1a) Imagine we have a sphere made of some sort of insulated material. Let's say that sphere has a charge of -2.5 C.

• What sort of information can you get from that situation using Gauss's Law?

We can create a spherical Gaussian Surface surrounding that sphere and use that to find the electric flux.

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#1b) Now add no more than 5 words to the previous question that would allow us to use Gauss's Law to find the Electric Field at some position outside of that shell.

Imagine we have a sphere made of some sort of insulated material. Let's say that sphere has a charge of -2.5 C uniformly distributed through the sphere.

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#1c) Explain the differences in verbiage between #1a and #1b

If the charge is uniformly distributed throughout the sphere we have the symmetry we need to be able to apply Gauss's Law.

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#1d) Consider the single-word change made to question #1a as follows:

Imagine we have a sphere made of some sort of conducting material. Let's say that sphere has a charge of -2.5 C.

How is it that we can easily use Gauss's Law to find the electric field at some position outside that sphere?

If the sphere is made out of a conducting material, the charges are all free to roam and will orient themselves to uniform distribution..... bringing us back to the symmetry we need to be able to use Gauss's Law to find the Electric Field.

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Let's make a double-extra effort to be intentional with our learning. Your MOST Gracious (and humble) physics instructor has henceforth and herewith provided the AP C learning targets for each of first 3 E & M units. Do you ever take a gander at those? (say YES!)

Anywho...

Here are the learning targets for our first three units Charges, Gauss, Volts. Please rate your understanding (from 1 - 5) for each target (Printable version is HERE)

 Charges Learning Targets Rating (A) Students should be able to use the principle of superposition to calculate by integration: (1) The electric field of a straight, uniformly charged wire. (2) The electric field and potential on the axis of a thin ring of charge, or at the center of a circular arc of charge (3) The electric potential on the axis of a uniformly charged disk. (B) Students should know the fields of highly symmetric charge distributions, so they can: (1) Identify situations in which the direction of the electric field produced by a charge distribution can be deduced from symmetry considerations (2) Describe qualitatively the patterns and variation with distance of the electric field of oppositely-charged parallel plates. (3) Describe qualitatively the patterns and variation with distance of the electric field of a long, uniformly-charged wire, or thin cylindrical or spherical shell. (4) Derive expressions for electric potential as a function of position in the above cases. Gauss Learning Targets (A) Students should understand the relationship between electric field and electric flux, so they can: (1) Calculate the flux of an electric field through an arbitrary surface or of a field uniform in magnitude over a Gaussian surface and perpendicular to it. (2) Calculate the flux of the electric field through a rectangle when the field is perpendicular to the rectangle and a function of one coordinate only. (3) State and apply the relationship between flux and lines of force. (B) Students should understand Gauss’s Law, so they can: (1) State the law in integral form, and apply it qualitatively to relate flux and electric charge for a specified surface. (2) Apply the law, along with symmetry arguments, to determine the electric field for a planar, spherical, or cylindrically symmetric charge distribution. (3) Apply the law to determine the charge density or total charge on a surface in terms of the electric field near the surface. Electric Potential/Potential Difference/Electric Potential Difference/ Volts FIELDS AND POTENTIAL OF OTHER CHARGE DISTRIBUTION (A) Students should be able to use the principle of superposition to calculate by integration: (1) The electric field of a straight, uniformly charged wire. (2) The electric field and potential on the axis of a thin ring of charge, or at the center of a circular arc of charge (3) The electric potential on the axis of a uniformly charged disk. (B) Students should know the fields of highly symmetric charge distributions, so they can: (1) Identify situations in which the direction of the electric field produced by a charge distribution can be deduced from symmetry considerations (2) Describe qualitatively the patterns and variation with distance of the electric field of oppositely-charged parallel plates. (3) Describe qualitatively the patterns and variation with distance of the electric field of a long, uniformly-charged wire, or thin cylindrical or spherical shell. (4) Derive expressions for electric potential as a function of position in the above cases.

(Printable version is HERE)

Now use this as a guideline to research/review/rewind/re-do topics that you need to brush up on.

Keep in mind, our book does MANY of these topics in the same order, but not all of them.