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Physics · Glossary

What is Electric field?

Definition 14.3 High School Physics · Chapter 14 — Electric and Gravitational Fields

If a small test charge qq placed at a point MM feels an electric force F→\vect F, the electric field at MM is

E→=F→q(in N/C, also written V/m).\vect E = \frac{\vect F}{q} \qquad \text{(in $\mathrm{N}/\mathrm{C}$, also written $\mathrm{V}/\mathrm{m}$)}.

E→\vect E depends only on the sources and on MM, not on the test charge: doubling qq doubles F→\vect F, leaving the quotient unchanged.

Examples

Example 14.5 (Reading a field)

A test charge q=2.0×10−8 Cq = 2.0 \times 10^{-8}\,\mathrm{C} at MM feels a force of 6.0×10−4 N6.0 \times 10^{-4}\,\mathrm{N} pointing east. The field at MM is E=6.0×10−4/2.0×10−8=3.0×104 N/CE = 6.0 \times 10^{-4} / 2.0 \times 10^{-8} = 3.0 \times 10^{4}\,\mathrm{N}/\mathrm{C}, pointing east; q′=−1.0×10−8 Cq' = -1.0 \times 10^{-8}\,\mathrm{C} placed at the same point feels F=1.0×10−8×3.0×104=3.0×10−4 NF = 1.0 \times 10^{-8} \times 3.0 \times 10^{4} = 3.0 \times 10^{-4}\,\mathrm{N} — pointing west.

Example 14.7 (A charged sphere)

A Van de Graaff sphere carries Q=5.0×10−7 CQ = 5.0 \times 10^{-7}\,\mathrm{C} (a small charged sphere acts like a point charge at its center). At d=0.50 md = 0.50\,\mathrm{m}:

E=8.99×109×5.0×10−7/0.502≈1.8×104 N/C,E = 8.99 \times 10^{9} \times 5.0 \times 10^{-7} / 0.50^2 \approx 1.8 \times 10^{4}\,\mathrm{N}/\mathrm{C},

pointing radially away from the sphere. At 1.0 m1.0\,\mathrm{m} it has dropped to a quarter of this: the 1/d21/d^2 of the force survives in the field.

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