A field assigns to every point of space a vector. A source (a charge, a mass) creates its field everywhere around it, whether or not anything is there to feel it; a test object then feels a force determined by the field at its own location alone. This two-step picture replaces action at a distance.
Examples
Example 14.5 (Reading a field)
A test charge q=+2.0×10−8C at M feels a force of 6.0×10−4N pointing east. The field at M is E=6.0×10−4/2.0×10−8=3.0×104N/C, pointing east; q′=−1.0×10−8C placed at the same point feels F=1.0×10−8×3.0×104=3.0×10−4N — pointing west.
Example 14.7 (A charged sphere)
A Van de Graaff sphere carries Q=+5.0×10−7C (a small charged sphere acts like a point charge at its center). At d=0.50m:
E=8.99×109×5.0×10−7/0.502≈1.8×104N/C,
pointing radially away from the sphere. At 1.0m it has dropped to a quarter of this: the 1/d2 of the force survives in the field.
Example 14.15 (The field where the Moon lives)
At the Moon’s distance d=3.84×108m:
g=6.67×10−11×5.97×1024/(3.84×108)2≈2.7×10−3N/kg.
Earth’s field never stops — it only thins out as 1/d2; this is the field that holds the Moon on its orbit.
Coach