Electrostatics: summary

1. Electrostatics: summary Electrostatics is the branch of E&M that deals with the phenomena arising from stationary electric charges. The fundamental equation of electrostatics is Coulomb's law, which describes the force between two point charges. The magnitude of the electrostatic force between two point electric charges is directly proportional to the product of the magnitudes of each charge and inversely proportional to the square of the distance between the charges Permittivity of free space (or electric constant) 8.854 187 817... × 10−12 A2 s4 kg−1 m−3 in SI base units in cgs base units

2. The principle of linear superposition may be used to calculate the force on a small test charge, q, due to a system of N discrete charges:

3. Continuous charge distribution For a charge distribution an integral over the region containing the charge is equivalent to an infinite summation, treating each infinitesimal element of space as a point charge dq. electric charge volume density Electric field trial charge Electric field produced by two point charges q =+4 The electric field can be represented graphically by field lines. These lines are drawn in such a way that, at a given point, the tangent of the line has the direction of the electric field at that point. The density of lines is proportional to the magnitude of the electric field. Each field line starts on a positive point charge and ends on a negative point charge

4. Example: Find the electric field a distance z above the center of a square loop of side a carrying uniform line charge l. P z a a Hint: find the electric field a distance z above the midpoint of a straight line segment of length 2L which carries a uniform line charge l. x=-L x=+L