Gauss s Law Simulation Activities

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Martin Boone
5 years ago
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1 Gauss s Law Simulation Activities Name: Backgound: The electic field aound a point chage is found by: = kq/ 2 If thee ae multiple chages, the net field at any point is the vecto sum of the fields. Fo a lage numbe of point chages distibuted unifomly on the suface o thoughout an object, Gauss s law is a convenient way of simplifying this calculation. Gauss s Law says that the electic flux, which is the dot poduct of the electic field and the suface aea of the Gaussian suface that encloses the chage, is equal to the amount of chage enclosed divided by the pemittivity of fee space: ˑ A = qenc/ε0 The aea vecto is pependicula to the suface aea, so a Gaussian suface is chosen so that the electic field passes though eithe pependicula o paallel to the suface. If the field is paallel to the suface, the flux is equal to zeo and if the field is pependicula to the suface, the dot poduct becomes simple multiplication: x A. Common Gaussian sufaces ae sphees, and cylindes, though othe shapes can be used. Simulation 1: Point Chage Befoe you stat, answe the following questions: 1. What shape would you choose fo you Gaussian suface? 2. On the gaphs below, pedict what you think the gaphs of flux v. adius and electic field v. adius will look like:

2 Now open the simulation fo the point chage. Pess Play and the Gaussian suface will expand with espect to the adius. Daw the gaphs you obseve below. 1. Why do you think the gaph looks the way it does? 2. What would you have to do to change the? 3. How would you descibe the lectic Field gaph? Is it consistent with what you know about point chages? Incease the amount of chage and dag the adius back to 0.1m. 4. Descibe any similaities and diffeences you see in the two gaphs. 5. What happens if you make the chage negative?

3 Simulation 2: Spheical Conducto Befoe you stat, answe the following questions: 1. What shape would you choose fo you Gaussian suface? 2. On the gaphs below, pedict what you think the gaphs of flux v. adius and electic field v. adius will look like: Now open the simulation fo the point chage. Pess Play and the Gaussian suface will expand with espect to the adius. Daw the gaphs you obseve below. 3. Why do you think the gaph looks the way it does? 4. How would you descibe the lectic Field gaph? Use Gauss s Law to explain why the field is zeo inside the conducto. Compae the field outside the conducto to the gaph seen with the point chage. Incease the amount of chage and dag the adius back to 0 m.

4 5. Descibe any similaities and diffeences you see in the two gaphs. 6. What happens if you make the chage negative? 7. The gaph expeiences a tansition at one paticula adius. What is special about this adius? Simulation 3: Sphee with a Unifom Chage Distibution Befoe you stat, answe the following questions: 1. What shape would you choose fo you Gaussian suface? 2. On the gaphs below, pedict what you think the gaphs of flux v. adius and electic field v. adius will look like:

5 Now open the simulation fo the point chage. Pess Play and the Gaussian suface will expand with espect to the adius. Daw the gaphs you obseve below. 3. Why do you think the gaph looks the way it does? 4. Why does the fist potion of this gaph look so diffeent fom what we have seen in the pevious two examples? 5. How would you descibe the lectic Field gaph? Why does the field incease at fist? Outside the sphee, how does the electic field compae to the pevious simulations? Use Gauss s Law to justify you answes. Incease the chage density and dag the adius back to 0 m. 6. Descibe any similaities and diffeences you see in the two gaphs. 7. What happens if you make the chage negative?

6 Simulation 4: Line of Chage Befoe you stat, answe the following questions: 1. What shape would you choose fo you Gaussian suface? 2. On the gaphs below, pedict what you think the gaphs of flux v. adius and electic field v. adius will look like: Now open the simulation fo the point chage. Pess Play and the Gaussian suface will expand with espect to the adius. Daw the gaphs you obseve below. 3. Why do you think the gaph looks the way it does? How could the amount of flux be changed? 4. Is thee any potion of the cylinde that expeiences a flux of zeo? Why/Why not?

7 5. How would you descibe the lectic Field gaph? Is it consistent with what you know about point chages? Incease the linea chage density and dag the adius back to 0.1m. 6. Descibe any similaities and diffeences you see in the two gaphs. 7. What happens if you make the chage negative?

Gauss Law. Physics 231 Lecture 2-1

Gauss Law. Physics 231 Lecture 2-1 Gauss Law Physics 31 Lectue -1 lectic Field Lines The numbe of field lines, also known as lines of foce, ae elated to stength of the electic field Moe appopiately it is the numbe of field lines cossing