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Electric fields summary

Key concepts of electric fields

An electric field created by a source charge creates a force at each point in a region of space. The strengths of different fields sum up to form a global field.

Coulomb's law between two point charges (dimensionless particles):

$$F=\frac{Q_{1}Q_{2}}{4\pi\epsilon_{0}r^{2}}$$

Electric field strength (on a test charge $q$) : $E=F/q$

• produced by a point charge $Q$ : $$E=\frac{Q}{4\pi\epsilon_{0}r^{2}}$$

Electric potential (work done by a unit charge) : $V=W/q$

Potential difference: $W= Q(V_{1}-V_{2})$

Direction of the electric field from higher potential to lower potential.

• produced by a point charge $Q$ : $$V=\frac{Q}{4\pi\epsilon_{0}r}$$

Uniform field strength between two plates:

$$E=\frac{V}{d}$$

Deflection of a charged particle moving through a uniform electric field.

$F=$magnitude of the force; $Q$, $q=$source and test point charges; $r=$distance between two charges; $\epsilon_{0}=$permittivity of free space; $d=$ distance between two charged plates.

Electric and gravitational field comparison

Gravitational and electric fields are similar in many respects.

Both forces are inversely proportional to the square of distance between the two masses/charges (i.e. they follow an inverse square law).

Both also involve the interaction of two bodies without direct contact (non-contact forces).

Gravity is always attractive, while electric fields can either attract or repel other charged objects depending on their charge.

Another significant difference is the magnitude of the forces. The electric force between two protons is $10^{36}$ times stronger than the gravitational force between them.

Gravitational fields Electric fields
Force $$F=G\frac{Mm}{r^{2}}$$ $$F=\frac{1}{4\pi\epsilon_{0}}\frac{Qq}{r^{2}}$$
Field strength $$g=G\frac{M}{r^{2}}$$ $$E=\frac{1}{4\pi\epsilon_{0}}\frac{Q}{r^{2}}$$
Potential $$V=G\frac{M}{r}$$ $$V=\frac{1}{4\pi\epsilon_{0}}\frac{Q}{r}$$