Electric Fields
Equations
\[F=\frac{1}{4\pi\varepsilon_{0}}\frac{Q_{1}Q_{2}}{r^2}$$
$$E=\frac{\Delta V}{d}$$
$$F=EQ$$
$$E=\frac{F}{Q}$$
$$W=\Delta VQ\]
Proportionality
\[E \propto V$$
$$E\propto\frac{1}{d}$$
$$F\propto E$$
$$F\propto Q\]
Two electrons are fired towards each other and reach a separation of 5.22 x 10^-13 m. What's the force on each electron at this point?
\[\frac{1}{4\pi\varepsilon_{0}}\times \frac{(-1.6\times10^{-19})^2}{(5.22\times10^{-13})^2}=8.44\times10^{-4}\]
The electric field generated by a charged sphere with charge 4.15 microcoulombs is measured as 15 000 NC^-1. How far from the centre of the sphere must the measuring instrument be?
\[\sqrt{ \frac{1}{4\pi \times E} \times \frac{4.15\times10^{-6}}{15000}}=1.57=1.6\]
Graph of a charge's force field
- Negative gradient = repulsive force
- Positive gradient = attractive force