Physics quiz archive: interference, electrostatics

Physics 205B Quiz 3, spring semester 2020
Cuesta College, San Luis Obispo, CA
Sections 30882, 30883, version 1
Exam code: quiz03Cv1d



Sections 30882, 30883 results

0- 6 :
7-12 :
13-18 :	**** [low = 15]
19-24 :	***************
25-30 :	*************** [mean = 24.2 +/- 4.2] [high = 30]

Physics quiz archive: interference, electrostatics

Physics 205B Quiz 3, spring semester 2019
Cuesta College, San Luis Obispo, CA
Sections 30882, 30883, version 1
Exam code: quiz03b3Am



Sections 30882, 30883 results

0- 6 :	** [low = 3]
7-12 :	**
13-18 :	*********
19-24 :	***************** [mean = 21.5 +/- 6.0]
25-30 :	************ [high = 30]

Physics quiz archive: interference, electrostatics

Physics 205B Quiz 3, spring semester 2018
Cuesta College, San Luis Obispo, CA
Sections 30882, 30883, version 1
Exam code: quiz03Ch4R



Sections 30882, 30883 results

0- 6 :
7-12 :	** [low = 9]
13-18 :	****
19-24 :	************ [mean = 23.3 +/- 4.9]
25-30 :	************** [high = 30]

Physics quiz archive: interference, electrostatics

Physics 205B Quiz 3, spring semester 2017
Cuesta College, San Luis Obispo, CA
Sections 30882, 30883, version 1
Exam code: quiz03d3St



Sections 30882, 30883 results

0- 6 :
7-12 :	* [low = 9]
13-18 :	*****************
19-24 :	******** [mean = 18.6 +/- 4.4]
25-30 :	** [high = 27]

Physics quiz archive: interference, electrostatics

Physics 205B Quiz 3, spring semester 2016
Cuesta College, San Luis Obispo, CA
Sections 30882, 30883, version 1
Exam code: quiz03Ccf7



Sections 30882, 30883 results

0- 6 :	** [low = 6]
7-12 :	***********
13-18 :	******
19-24 :	*************** [mean = 18.8 +/- 7.2]
25-30 :	****** [high = 30]

Presentation: electric potential energy

Look at all these batteries. Just look at them. While we might think of them as "containing" electrical potential energy, or even as voltage "sources," we'll see that just two charges can "contain" electric potential energy, and that just a single charge can be thought of as a voltage "source." In subsequent presentations we'll explore more complex voltage "sources" that "contain" electric potential energy: capacitors, batteries, and household electric outlets.

In this presentation we will consider different approaches to analyze electric potential energy.

First, a direct approach to electric potential energy.

Recall that in the direct approach to electric forces, a source charge q₁ can be said to exert a force F on a separate test charge q₂.

Similarly, a direct approach to electric potential energy is that a source charge q₁ can be said to store electric potential energy EPE on with a separate test charge charge q₂.

∆EPE changes in this electric potential energy are caused by moving the source charge and test charge closer together, or moving them farther apart. EPE can be increased (thus making ∆EPE positive) by pushing together like-sign charges (positive-positive, or negative-negative), or pulling apart opposite-sign charges (positive-negative, or negative-postive). This is because it takes work to push together like-sign charges (which repel, and don't want to be pushed together); or takes work to pull apart opposite-sign charges (which attract, and don't want to be pulled apart).

On the other hand, work is done by charges that are allowed to do what they want to, thus decreasing EPE (and making ∆EPE negative), by letting like-sign charges (positive-positive, or negative-negative) move farther apart from each other (because these charges repel); or letting opposite-sign charges (positive-negative, or negative-positive) move closer to each other (because these charges attract).

The value of the electric potential energy of a source charge q₁ and test charge q₂ at a certain distance r from each other can be calculated by an equation that looks similar to the magnitude of the electric force (but note the r^–1 dependence for electric potential energy, as opposed to the r^-2 dependence of electric forces). With the constant k, units of coulombs² and meters cancel, leaving units of N·m, which is what we have seen last semester as joules.

(Note that this equation calculates the value of electric potential energy EPE of two charges at a fixed separation distance from each other. In order to find the ∆EPE change in electric potential energy, you would need to calculate the initial EPE_i and final EPE_f electric potential energies of the two charges at their initial r_i and final r_f separation distances.)

Second, the two-step approach to electric potential energy.

Recall that in the two-step approach to electric forces, a source charge Q can be said to create an electric field E everywhere around itself, and then this electric field exerts a force F on a separate test charge q.

Similarly, a two-step approach to electric potential energy is that a source charge Q can be said to create a potential V everywhere around itself, and this potential stores electric potential energy EPE with a separate test charge charge q.

Let's focus on the first step of this two-step model. The source charge Q creates a potential V everywhere around it. The magnitude of this potential can be calculated for a location at a distance r from the source charge, and has units of joules per coulomb (J/C), which is often re-expressed as volts (V). The sign of the potential depends on the sign of the source charge Q: if the source charge is positive, then the values of the potential everywhere around it are positive; if the source charge is negative, then the values of the potential everywhere around it are negative.

Recall that electric fields surrounding a single source charge are visualized as lines emanating outwards from, or pointing in towards the source charge. In contrast, the potentials surrounding a single source charge are visualized (here, in two-dimensions) as circles, as every location at the same distance r from the source charge must have the same value of potential, such that these circles are often referred to as equipotentials.

Note that the direction of electric field lines is indicative of the relative values of the equipotentials: for the positive source charge, each subsequent outer equipotential corresponds to smaller and smaller positive values of potential (due to the r^–1 dependence); for the negative source charge, each subsequent inner potential equipotential corresponds to larger and larger negative values of potential. So in either case, electric field lines point towards decreasing electric potential values.

A nice visualization is to imagine that a positive source charge creates a "peak" of potential around it--as you get closer in towards this positive source charge, the values of potential become bigger and bigger positive numbers, corresponding to a increase in elevation. In contrast, a negative source charge creates a "well" of potential around it--as you get closer in towards this negative source charge, the values of potential become bigger and bigger negative numbers, corresponding to a decrease in elevation.

So where does "voltage" come in? The amount of potential (which is measured in volts) at a location in space is often called the "voltage." So "potential" and "voltage" really mean the same thing (and just to confuse things even further, "electrical tension" is an equivalent archaic term). Get used to these terms, as we will be referring to them interchangeably through the remainder of this semester. Nobody ever thinks this is a big deal, so deal with it. (But yes, it is a big deal.)

Now what? If there is another charge anywhere in the presence of a potential, this potential will store electrical potential energy with the test charge q. In this equation, the electrical potential energy EPE stored by the test charge q is the test charge q multiplied by the potential V at the test charge's location. Since the test charge q could be positive or negative, and the potential V could have positive or negative values, then the electrical potential energy stored would have the correct sign depending the the product of these two signs.

(Notice that coulombs (C) multiplied by volts (V, or J/C) results in units of joules (J). In this sense potential or "voltage" can be said to be "potential" potential energy, that is, a location in space will only have a value for potential (measured in volts, or joules per coulomb), but any test charge q placed at this location in space will then have a value for electric potential energy (measured in joules) given by the product of the potential and amount of charge placed there.)

Here, from before, we show the electrical fields and potentials filling in all space surrounding a positive or a negative source charge. Putting a positive test charge in the presence of these electrical fields and potentials will cause an electrical force to be exerted along a field line, which would also point in the direction of decreasing potential and decreasing potential energy; while putting a negative test charge in the presence of these electrical fields and potentials will cause an electrical force to be exerted in the opposite direction of a field line, which would point in the direction of increasing potential, but decreasing potential energy.

In any case, as a check the direction of the force on any source charge q should be attractive or repulsive depending on whether it has the opposite or same sign as the source charge Q, and also check that the source charge q moves in the direction that would decrease its electric potential energy. However, positive test charges move in the direction of decreasing potential, while negative test charges move in the direction of increasing potential! (If all this sounds confusing, at least be assured that these rules are consistent.)

As previously above, we visualized a positive source charge +Q as a "peak." Here we have a positive test charge +q as a hapless snowmobiler on this "peak." Initially as the snowmobiler rides up the "peak," increasing his potential and increasing his potential energy, work is required to push it "uphill" (provided by an external source, here the snowmobile engine). Left alone, the snowmobile and snowmobiler will slide "downhill," in the direction of decreasing potential and decreasing potential energy (as we have seen before, for two positive charges separating from each other). What would happen if the snowmobiler were a negative test charge –q? Then we would observe the very odd behavior of this negative snowmobiler sliding "uphill," in the direction in increasing potential--but this would be the direction of decreasing potential energy, as we have seen before, for a negative charge and a positive charge getting closer to each other.

What would happen if there was a negative source charge –Q creating a "well?" Then a positive test charge +q snowmobiler, left alone, would slide "downhill," in the direction of decreasing potential and decreasing potential energy (as we have seen before, for a negative charge and positive charge getting closer to each other). Then consider the very odd case of a negative test charge –q snowmobiler sliding on this "well"--we would observe the very odd behavior of this negative snowmobiler sliding "uphill," in the direction in increasing potential--but this would be the direction of decreasing potential energy, as we have seen before, for two negative charges separating from each other. (Video source: "Grazy hill climb crash with go pro cam.")

Physics quiz archive: interference, electrostatics

Physics 205B Quiz 3, spring semester 2015
Cuesta College, San Luis Obispo, CA
Sections 30882, 30883, version 1
Exam code: quiz03wJnb



Sections 30882, 30883 results

0- 6 :	****** [low = 0]
7-12 :	*****
13-18 :	****************** [mean = 16.7 +/- 7.2]
19-24 :	***********
25-30 :	**** [high = 30]

Physics quiz archive: interference, electrostatics

Physics 205B Quiz 3, spring semester 2014
Cuesta College, San Luis Obispo, CA
Sections 30882, 30883, version 1
Exam code: quiz03cDvD



Sections 30882, 30883 results

0- 6 :
7-12 :	*** [low = 9]
13-18 :	*******************
19-24 :	************* [mean = 19.7 +/- 5.0]
25-30 :	***** [high = 30]

Physics quiz archive: interference, electrostatics

Physics 205B Quiz 3, spring semester 2013
Cuesta College, San Luis Obispo, CA
Section 30882, version 1
Exam code: quiz03rD1o



Section 30882 results

0- 6 :
7-12 :	****** [low = 9]
13-18 :	********
19-24 :	************* [mean = 19.9 +/- 5.5]
25-30 :	***** [high = 30]

Presentation: electric forces and fields

Look at this van de Graff generator exerting attractive and repulsive forces on these soap bubbles. Just look at it. (Video link: "Static Electricity and Bubbles!")

While we will quantify how charges exert electric forces on other charges, consider the philosophical problem of why charges are able to exert electric forces on other charges, without touching, across empty space. This is the action-at-a-distance problem. We are going to "solve" this problem in this presentation--well, sort of--and much later will only be able to completely "solve" the action-at-a-distance problem near the end of this semester by introducing the concept of quantum electrodynamics.

In this presentation we will discuss two models of how charges exert electric forces on other charges.

First, a "direct" model of electric forces.

By convention we label the two charges that exert forces on each other as "source" and "test" charges, where the source charge q₁ is said to be exerting a force on the test charge q₂. This force is attractive if the source charge and test charge have opposite signs, and repulsive if the source charge and test charge have the same sign.

Coulomb's law quantifies the magnitude of the force that a source charge exerts on a test charge, separated by a distance r. Note that the signs of the charges do not matter when calculating the magnitude of the force, and that the constant k handles unit cancellation and conversion to express the force with the proper units of newtons.

Second, an "indirect" or two-step model of electric forces.

Here the convention is to label the source charge and test charge as Q and q, respectively. Instead of the source charge Q directly exerting a force on the test charge q, in this two-step model, the source charge Q is said to create an electric field everywhere around it, and it is this electric field that exerts a force on a test charge q.

Let's focus on the first step of this two-step model. The source charge Q creates an electric field everywhere around it. The magnitude of this electric field can be calculated for a location at a distance r from the source charge, and has units of newtons per coulomb (N/C). The direction of this electric field depends on the sign of the source charge Q: if the source charge is positive, the electric field vectors point outwards from it; if the source charge is negative, the electric field vectors point in towards it.

An electric field is depicted as filling in all space surrounding a source charge, and is drawn as field lines that point outwards from a positive source charge, and point in towards a negative source charge.

Now what? If there is another charge anywhere in the presence of an electric field, this electric field will exert a force on the test charge q. Note that this is a vector equation, where the force F (magnitude and direction) exerted on the test charge q is the test charge q multiplied by the electric field E (magnitude and direction) at the test charge's location. Since the test charge q could be positive or negative, then the electric force exerted on it could have the same or opposite direction as the electric field lines.

Here, from before, we show the electric fields filling in all space surrounding a positive or a negative source charge. Putting a positive test charge in the presence of these electric fields will cause an electric force to be exerted along a field line, while putting a negative test charge in the presence of these electric fields will cause an electric force to be exerted in the opposite direction of a field line. (In any case, as a check the direction of the force on any source charge q should be attractive or repulsive depending on whether it has the opposite or same sign as the source charge Q.)

So if using Coulomb's law in the direct model of calculates the electric force a source charge exerts on a test charge, why do we need a two-step model of a source charge generating a field, and this field exerting an electric force on a test charge?

Here in this excerpt from Star Wars Episode IV: The Empire Strikes Back (Lucasfilm/Twentieth Century Fox, 1980), Luke Skywalker is trying to grab his lightsaber, which is just beyond is reach. He could use the "force" to pull his lightsaber, but this brings up the philosophical problem of how a force of one object on another can be exerted across empty space.

Instead, let's reinterpret this in terms of the two-step field model. Luke goes into a trance, and let's say that he is generating some sort of field around himself (as Obi-Wan Kenobi explains: "...an energy field created by all living things. It surrounds us and penetrates us; it binds the galaxy together"). This field spreads out from and surrounds Luke, and it is this field that exerts a force on the lightsaber, pulling it out of the snowbank. Mayhem ensues.

So now we've "solved" the action-at-a-distance problem here by discussing a field as occupying the empty space surrounding and between the source object (Luke) and the test object (the lightsaber). (Perhaps, then, Luke is really using the "Field," and not the "Force" in the Star Wars universe.) And we put "solved" in quotes because this really recasts the philosophical action-at-a-distance problem as a philosophical question of what exactly is a field (and is it really generated by and surrounds a source object)? In a subsequent presentation near the end of this semester we will explain the physical nature of what a field is, but for now we will merely take an electric field as a given in our two-step model of how charges exert electric forces on other charges.

In this discussion we only considered the force exerted by a single source charge on a test charge, or the field generated by a single source charge. Later in class we will go through more complex situations where there may be multiple source charges, each exerting forces on the same test charge (thus requiring us to determine the net force on the test charge); or multiple source charges, each creating an electric field at the same location in space (thus requiring us to determine the net electric field at that location). So be sure to brush up on one-dimensional vector addition, as discussed last semester.

So remember, may the field be with you...