Partnership for Integration of Computation into Undergraduate Physics

## Exercise 1 Write the pseudo code to compute and plot the electric field on a meshgrid. ## Exercise 2 Plot the electric vector field for a positive point charge using a $7\times7\times7$ meshgrid. Do the same for a negative point charge. ## Exercise 3 Plot the on-axis electric field versus distance from center of a uniformly charged ring with a linear charge density of $\lambda = \frac{10}{2\pi R}$, where $R$ is the radius of the ring. Recall the electric field for a uniformly charged ring is: $\overrightarrow{E}=k\frac{2\pi R\lambda z}{(R^2+z^2)^{3/2}}\hat{z}$ where $k$ is the Coulomb constant, $R$ is the radius of the ring, and $z$ is the on-axis coordinate. ## Exercise 4 Plot the electric field vectors in 3D for N number of positive point charges (discrete ring of charges). The N charges should be equidistant from each other and lie on a circle. For example, for N=2, the charges would lie on the ends of the diameter of the circle, i.e. 180 degrees from each other. See Theory section on Discrete Ring of Charges for illustration of N=4. Start with N = **2** and use a $7\times7\times7$ meshgrid. Do the same for : * N=**5** * N=**10** * N=**100** for a $7\times7\times7$ grid. Compare the electric field on-axis results to the analytical expression found in **Excercise 3** and explain your observations. Make sure to change the linear charge density $(\lambda=\frac{N}{2\pi R})$. ***Note***: You will have to look at electric field values, both for discrete charges and the continuous ring, on the meshgrid vertices. That means for more values, you have to increase the meshgrid space. Try a size of $27\times27\times27$ and see how that compares with the smaller meshgrid space of $7\times7\times7$. ## # Power of Computational Physics: Other Charge Configurations ## ## Excercise 5 Now assign alternating negative charges (indicate with a red color) and positive charges (indicate with blue color) around the ring. Show electric field vectors in 3D for N number of charges, as follows: * N=**5** * N=**10** * N=**100** for a $7\times7\times7$ grid. ## Exercise 6 Now assign one half of the ring with negative charges (red) and the other half of the ring with positive charges (blue). Show electric field vectors in 3D for N number of charges, as follows: * N=**5** * N=**10** * N=**100** for a $7\times7\times7$ grid. ## Exercise 7 Now assign one fourth of the ring with negative charges (red) and the next fourth of the ring with positive charges (blue), and so on. Show electric field vectors in 3D for N number of charges, as follows: * N=**4** * N=**16** * N=**100** for a $7\times7\times7$ grid.