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# Differences

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whitepapers:sequences:scalarfieldseq 2019/07/21 12:10 | whitepapers:sequences:scalarfieldseq 2019/07/22 06:58 current | ||
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We prefer to start upper-division E & M with electrostatic potential $V$ before electric field $\vec{E}$. This choice allows students to struggle with the simpler idea of a scalar field (a number at every point in space) before moving on to the more complicated idea of a vector field (a vector at every point in space). To use this sequence in this way, it is necessary to direct students to avoid (temporarily) using reasoning about electric fields and electric field lines, in order to build up intuition about the relationship between charged sources and electrostatic potentials. A little later, during a review of electric fields, the relationship between potential and electric field can also be reinforced. | We prefer to start upper-division E & M with electrostatic potential $V$ before electric field $\vec{E}$. This choice allows students to struggle with the simpler idea of a scalar field (a number at every point in space) before moving on to the more complicated idea of a vector field (a vector at every point in space). To use this sequence in this way, it is necessary to direct students to avoid (temporarily) using reasoning about electric fields and electric field lines, in order to build up intuition about the relationship between charged sources and electrostatic potentials. A little later, during a review of electric fields, the relationship between potential and electric field can also be reinforced. | ||

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- | The first two activities, [[swbq:emsw:vfswpointpot|Electrostatic Potential due to a Point Charge]] and [[courses:activities:vfact:vfdrawquadrupole|Drawing Equipotential Surfaces]], can be paired together with little introduction. The third and fourth activities, [[courses:activities:vfact:vfvisv|Visualizing Electrostatic Potentials]] and FIXME (Surfaces), introduce new representations of scalar fields using the same charge distributions as [[courses:activities:vfact:vfdrawquadrupole|Drawing Equipotential Surfaces]] and can be used as effective follow-ups to that activity. These four activities can be used effectively in immediate succession. FIXME (Does the surfaces project have a paper recommending a particular sequence?) | ||

- | The last activity [[courses:activities:vfact:vfvpoints|Electrostatic Potential Due to a Pair of charges]] is the capstone of the sequence. It benefits from some extra set-up on the distance formula which can be accomplished by the [[courses:activities:vfact:vfstartrek|Star Trek]] activity. | ||

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* **[[courses:activities:vfact:vfvpoints|Electrostatic Potential due to a Pair of Charges]]** //(Estimated time: 30 minutes, 50 minutes with optional power series extension)//: Students are asked to find (algebraically) the electrostatic potential on the axis and in the plane of two point charges using the superposition principle. To accomplish this, students need to figure out to use the equation for the potential due to a point charge that is not at the origin. If appropriate for the course, this activity can conclude with student using power series approximations to calculate formulas for an approximation to the potential near the origin or far from the charges. | * **[[courses:activities:vfact:vfvpoints|Electrostatic Potential due to a Pair of Charges]]** //(Estimated time: 30 minutes, 50 minutes with optional power series extension)//: Students are asked to find (algebraically) the electrostatic potential on the axis and in the plane of two point charges using the superposition principle. To accomplish this, students need to figure out to use the equation for the potential due to a point charge that is not at the origin. If appropriate for the course, this activity can conclude with student using power series approximations to calculate formulas for an approximation to the potential near the origin or far from the charges. | ||

+ | ==== Implementation ==== | ||

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+ | The first two activities, [[swbq:emsw:vfswpointpot|Electrostatic Potential due to a Point Charge]] and [[courses:activities:vfact:vfdrawquadrupole|Drawing Equipotential Surfaces]], can be paired together with little introduction. The third and fourth activities, [[courses:activities:vfact:vfvisv|Visualizing Electrostatic Potentials]] and FIXME (Surfaces), introduce new representations of scalar fields using the same charge distributions as [[courses:activities:vfact:vfdrawquadrupole|Drawing Equipotential Surfaces]] and can be used as effective follow-ups to that activity. These four activities can be used effectively in immediate succession. FIXME (Does the surfaces project have a paper recommending a particular sequence?) | ||

+ | The last activity [[courses:activities:vfact:vfvpoints|Electrostatic Potential Due to a Pair of charges]] is the capstone of the sequence. It benefits from some extra set-up on the distance formula which can be accomplished by the [[courses:activities:vfact:vfstartrek|Star Trek]] activity. | ||