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10.1.7: Summary

• • Contributed by Physics 7
• Physics at UC Davis

This chapter has introduced many new ideas related to fields, using the gravitational field as the primary example. In the upcoming chapters the electric and magnetic fields are also discussed, so do not be concerned that their treatment in this chapter was brief. The main concepts introduced were:

1. That a field is a physical quantity that exists and has a well-defined value in all of space. A field can change its value in space and in time, so the value of a field is a function both of time ($$t$$) and position ($$x$$ or $$r$$).

2. A force is an interaction between two objects. A field is created by a single object. All objects that feel a field must emit a field of the same type (like mass or electric charge). In Physics 7C, objects do not respond to their own field.

3. The fields we explore are mostly vector fields, meaning that at every point in space the field has a defined direction and magnitude.

4. When using the field model, one object (the “test” object) feels the field created by everything else (the “source” objects). We typically only explore circumstances where the effect of the test object's field on the source objects is ignored.

5. To find the field created by an arbitrary distribution of "sources," we use superposition.

6. Representations of vector fields

• Vector Map: A “snapshot” of some field vectors at a particular time. (e.g. wind map)

• Field Line Map: A “snapshot” of the field, but with continuous lines. The direction of the field at any point is tangent to the field lines. The strength of the field lines is determined by how close together the field lines are. If they are bunched up the field is strong, if they are spread thinly the field is weak.

• Equipotentials (not for magnetic fields): If a potential exists, then the equipotentials are lines where the potential is all the same. If we move along the equipotentials, we are not going “with” or “against” the field, and we don't gain or lose any energy. The equipotentials are always at 90° to the field lines. (e.g. a topographical map shows the equipotentials of a gravitational field)

7. An electric field line starts on a positive charge and ends on a negative charge.

8. A gravitational field line starts at infinity and ends on a mass.

9. Magnetic field lines form complete loops; they never start or end.