5.3.3: Problems

Exercise \(\PageIndex{1}\): Rank the point charges

The bar graph displays the electric flux passing through the cylindrical Gaussian surface (position is given in meters and flux is given in \(\text{N}\cdot\text{m}^{2}\text{/C}\)). Drag the surface and, from the flux readings, rank the charges from greatest to smallest. Restart.

Exercise \(\PageIndex{2}\): Rank the line charges

The bar graph displays the electric flux passing through the cylindrical flux detector (position is given in meters and flux is given in \(\text{N}\cdot\text{m}^{2}\text{/C}\). Drag the surface and observe the flux readings. Rank the charges (lines of charge extending into and out of the screen) from most negative to most positive. Restart.

Note

The Gaussian surface encloses two or three charges at a time. It never partially encloses a line charge.

Exercise \(\PageIndex{3}\): Describe the charge density

The bar graph displays the electric flux passing through the cylindrical Gaussian surface (position is given in meters and flux is given in \(\text{N}\cdot\text{m}^{2}\text{/C}\)). Drag the surface and from the flux readings and describe the charge distribution. Restart.

Exercise \(\PageIndex{4}\): Different size flux detectors to describe a hidden charge density

The bar graph displays the electric flux passing through a cubical flux detector and several spherical flux detectors. Drag each detector and observe the flux readings (position is given in meters and flux is given in \(\text{N}\cdot\text{m}^{2}\text{/C}\)). Describe the charge distribution in as much detail as possible. The resolution of the detector is \(1\text{ mC}\), and the gray sphere is there for your reference only. Restart.

Exercise \(\PageIndex{5}\): Determine flux through spherical shells

Three spherical shells (red, green, and blue) are located on the screen. You can only see the part of the sphere that is in the plane of the page. A test charge is also shown that measures the electric field at that point (position is given in meters and electric field strength is given in newtons/coulomb). Calculate the flux through each spherical shell. You can click-drag on the test charge to change its position. Restart.

Problem authored by Mario Belloni and modified by Anne J. Cox.

Exercise \(\PageIndex{6}\): Determine flux through a box

The green square represents a cross section of a cube. Use the test charge to explore the direction of the electric field inside the cube (position is given in meters and electric field strength is given in newtons/coulomb). Click-drag the cursor anywhere inside the cube to measure the magnitude of the electric field. Find the flux through the top, bottom, left, and right sides of the cube. Restart.

Problem authored by Evelyn Patterson and Scott Bonham and modified by Anne J Cox.

Exercise \(\PageIndex{7}\): Describe Gaussian surfaces for a capacitor

Each "charge" represents a long charged rod that extends into and out of the screen (position is given in meters). Restart.

1. Explain the electric field you see when the capacitor (long parallel sheets of charge) is complete.
2. The top and bottom sheets have equal and opposite charge. Which one is positively charged? Which is negatively charged?
3. What type of Gaussian surface would you use to find the field inside the capacitor? What type would you use outside the capacitor?
4. Sketch the Gaussian surface and explain why you chose it.

Problem authored by Wolfgang Christian, Melissa Dancy and Anne J Cox.

Exercise \(\PageIndex{8}\): Symmetry and field at distances far away

Although electric fields can be quite complicated close to a charge distribution, they often become very simple at large distances (position is given in meters and electric field strength is given in newtons/coulomb). Restart.

1. What symmetries does each of these configurations have at large distances?
2. When possible, find an analytical expression for the field at large distances using Gauss's law for each configuration.

Note

Note that each configuration contains either point charges or line charges (into and out of the screen), but not both. You can measure the electric field strength by click-dragging in the animation.

Exercise \(\PageIndex{9}\): Line of charge or sheet of charge?

Which configuration (when complete) represents a line of charge, and which represents a sheet of charge (where the points you see on the screen extend into and out of the screen)? Explain your reasoning. You can read the value of the electric field at any point by clicking with your mouse into the screen of interest (position is given in meters and flux is given in \(\text{N}\cdot\text{m}^{2}\text{/C}\)). Restart.

Problem authored by Anne J. Cox.
Script authored by Wolfgang Christian.

Exercise \(\PageIndex{10}\): Charge on coaxial cable using Gauss's Law

In this animation each charge represents a line or rod of charge extending into and out of the computer screen (position is given in centimeters and electric field strength is given in newtons/coulomb). Restart.

1. Explain how you know that the charge on the inner rod and the total charge on the outer cylinder are equal and opposite.
2. From the electric field measurements (read values when you drag the mouse on the screen), find the value of the charge per unit length, \(\lambda\), as well as an expression for the electric field as a function of \(\lambda\) at any point. (The charge per unit length, \(\lambda\), is the total charge \(Q\) divided by the length of the object \(L\).)

Problem authored by Anne J. Cox.
Script authored by Wolfgang Christian.

Exercise \(\PageIndex{11}\): Charge on capacitor using Gauss's Law

Each "charge" represents a long charged rod that extends into and out of the screen (position is given in centimeters and electric field strength is given in newtons/coulomb). Restart.

1. Add the top plate of the capacitor. Measure the electric field close to the top plate and then use Gauss's law to find the charge/area on the plate.
2. Do the same for the bottom plate.
3. What is the field near the center of the completed capacitor?

Problem authored by Anne J Cox.
Script authored by Wolfgang Christian.

Exercise \(\PageIndex{12}\): Spherical charge distribution with Gauss's law

The graph shows the flux through the expanding spherical surface (position is given in centimeters, time is given in seconds, and flux is given in \(\text{N}\cdot\text{cm}^{2}\text{/C}\)). Push "play" to start the shell's expansion. Restart.

1. Describe the spherical charge distribution.
2. Find the equation of the electric field for the two charge distributions.

Problem authored by Anne J. Cox.

Physlets were developed at Davidson College and converted from Java to JavaScript using the SwingJS system developed at St. Olaf College.