Summary Chapter 17: Electric Fields and Potential
- There are two types of charges. They are the positive charges and the negative charges.
- Electric force exists between a pair of charges. Like charges repel and unlike charges attract.
Coulomb’s Law
$F = \frac{1}{4πε_0}\frac{ Q_1Q_2}{r^2}$
(in free space)
Electric Field
- An electric field is a region in which an electric force will act on a charge that is placed at any point in the region.
- The electric field strength at a point in an electric field is defined as the electric force per unit charge experienced by a charge placed at that point.
- The electric field strength E at a point is given by
$E = \frac{F}{q}$
- The electric field strength E at a point in an electric field produced by an isolated point charge Q is given by
$E = \frac{Q}{4πε_0 r^2}$
(in free space)
Electric Flux and Gauss’ Law
- The electric flux Φ flowing through an area ΔA is given by
$Φ = EΔA \ cos \ θ$
- Gauss’ law states that the total electric flux Φ flowing through a surface of arbitrary shape that encloses completely a charge Q within that surface and in free space is equal to Q/ε0, i.e.
$Φ = \frac{Q}{ε_0}$
(in free space)
Electric Potential
- The electric potential V at a point in an electric field is given by
$V = \frac{U}{q}$
where U is the electric potential energy of a charge q found at the point.
- The electric potential at infinity is taken to be zero, i.e. V∞ = 0.
- The potential difference ΔV across points X and Y is the energy required to transfer 1 C of positive charge from X to Y.
- The electric potential difference ΔV is given by
$ΔV = \frac{W}{q}$
where W is the work done on charge q.
- The electric potential V at a point in an electric field produced by an isolated point charge Q is given by
$V = \frac{Q}{4πε_0 r}$
(in free space)
Electric Force and Field Gradient
- The electric force F acting on a point charge along the x-axis is given by
$F = -\frac{dU}{dx}$
where U is the electric potential energy of the charge.
- The electric field strength E at a point along the x-axis is given by
$E = -\frac{dV}{dx}$
where V is the electric potential at the point.
Uniform Electric Field Between Plates
- The electric field strength at a point in the space between a pair of parallel oppositely charged plates is given by
$E = \frac{V}{d}$
where V is the potential difference between the plates separated by a distance d.
Energy Conservation in Electric Field
- The total energy of a point charge q moving in an electric field is conserved:
$K_A + qV_A = K_B + qV_B$
Electron-Volt
- The electron-volt is defined as the gain in energy by a particle carrying electronic charge that accelerates across an electric potential difference of 1 volt.
Equipotential Surface
- An equipotential surface is a surface where any point on it has the same electric potential.
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