# Lesson 13: Faraday's E&M Fields

```{Note}
The field idea
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"All the mathematical sciences are founded on relations between physical laws and laws of numbers, so that the aim of exact science is to reduce the problems of nature to the determination of quantities by operations with numbers. *On Faraday’s Lines of Force* (1856) a little unrefined for Cambridge Trinity College, but expected to do well: “He (Hopkins) was talking to me this evening about Maxwell. He says he is unquestionably the most extraordinary man he has met with in the whole range of his experience; he says it appears impossible for Maxwell to think incorrectly on physical subjects; that in his analysis, however, he is far more deficient; he looks upon him as a great genius, with all its eccentricities, and prophesies that one day he will shine as a liable in physical science, a prophecy in which all his fellow-students strenuously unite.”<br><br>

James Clerk Maxwell


```{admonition} &nbsp; Goals of this lesson:
Understanding, Appreciation, and Familiarity
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**I'd like you to Understand:**

* How the local interaction of a field is what matters in an electromagnetic interaction among charges and currents

* How to determine the shape of electric field from a configuration of electric charges

* How to determine the shape of a magnetic field from a configuration of currents

* How to calculate the potential energy and kinetic energies of charged objects in an electric field

**I'd like you to Appreciate:**

* How vector fields combine graphically

* That electric fields store energy

* How an electric field is defined from the electric force

* How the voltage relates to the potential energy in a parallel plate capacitor

**I'd like you to become Familiar With:**

* How we can visualize fields in demonstrations with iron filings and "dielectric" specks of matter