Recap of Chapter 21-24

Electric Charge and Electric Field

• There are two kinds of electric charge. Positive and negative.
• Charge is to be treated algebraically. It's unit is Coulombs (C).
• Electric charge is conserved
• Charge of an electron $-e=-\mathrm {e^{-}} =-1.6\times 10^{-19}{\textrm {C}}$

Coulomb's law:

• The magnitude of the force one point charge exerts on another is proportional to the product of their charges, and inversely proportional to the square of the distance between them.

$F=k{\frac {Q_{1}Q_{2}}{r^{2}}}={\frac {1}{4\pi \epsilon _{0}}}{\frac {Q_{1}Q_{2}}{r^{2}}}$

Electric Field

• The electric field, ${\vec {E}}$, due to one one or more charges, is defined as the force per unit charge that would act on a positive test charge $q$ placed at that point:

${\vec {E}}={\frac {\vec {F}}{q}}$

• The magnitude $\left|{\vec {E}}\right|=E$ is

$E=k{\frac {Q}{r^{2}}}$

• The total electric field at a point of space is equal to the vector sum of the individual fields (principle of superposition)
• Electric field lines start on positive charge, and terminate on negative charge. Their direction indicates the direction of force a positive test charge would feel (i.e. at each point of space, it is the vector sum of all ${\vec {E}}$). The intensity of the ${\vec {E}}$ is proportional to number of electric field lines drawn per unit space.
• The static electric field inside a conductor is zero, since the free electrons in the conductor would keep on moving freely until the field is zeroed.

Electric Dipole

• An electric dipole is a combination of two equal but opposite charges $+Q$ and $-Q$ separated by a distance $l$.
• The dipole moment is

$p=Ql$

• A dipole placed in a uniform electric field experiences a torque.
• The electric field produced by the dipole decreases as the third power of the distance $r$ from the dipole ($E\propto 1/r^{3}$ when $r\gg l$)

Gauss's Law

Electric Flux

• The electric flux $\Phi _{E}$ passing through an area $A$ is

 $\Phi _{E}$=\int\vec{E}\cdot d\vec{A}</math> 

where ${\vec {A}}$ is a vector with a magnitude equal to the the infinitesimal area in question, and direction along the unit normal (the vector that points outward from the enclosed surface).

• The flux through a surface is proportional to the number of field lines passing through it.

Gauss's law

• Gauss's law states that the net flux passing through any closed surface is equal to the net charge $Q_{\textrm {encl}}$ enclosed by the surface divided by $\epsilon _{0}$

$\oint {\vec {E}}\cdot d{\vec {A}}={\frac {Q_{\textrm {encl}}}{\epsilon _{0}}}$