Electric Field - Intensity of Electric Field

In practice, even a small test charge can disturb the field being measured. To eliminate this error, the intensity is defined more rigorously using a limiting process:
\[\vec{E}=\lim_{q_0\to0}\frac{\vec{F}}{q_0}\]

Why the limit is needed: As q₀ → 0, the test charge becomes negligibly small, so it does not alter the distribution of the source charge(s) creating the field. This gives the true field intensity at that point, independent of the test charge used to measure it.

• Electric field intensity is a vector quantity — force (\[\vec{F}\]) is a vector, and charge (q₀​) is a scalar, so their ratio is a vector.
• Direction: Same direction in which a positive test charge would tend to move if placed at that point.
• If the source charge is positive, \[\vec E\] points away from it; if negative, \[\vec E\] points towards it.

For a point charge q at distance r:

E = \[\frac{1}{4\pi\varepsilon_0}\cdot\frac{q}{r^2}\]

where \[\dfrac{1}{4\pi\varepsilon_0} = 9 \times 10^9 \, \text{N·m}^2/\text{C}^2\]

Think of electric field intensity like the "pull" felt by a leaf near a fan — the closer the leaf (test charge) is to the fan (source charge), the stronger the pull (force) it feels per unit of its own "responsiveness." The field exists whether or not the leaf is there; the leaf only helps us measure it.