Part 2: Electric Field Generation and Streamlines

Flashcards covering key definitions, symmetries, calculation methods, and visualizations related to electric fields from continuous charge distributions, as discussed in the lecture.

Radial Symmetry

A type of symmetry where the electric field due to a point charge at the origin only varies with respect to the distance between the point charge and the evaluation point.

Infinitesimal Charge (dQ)

A small, differential unit of charge used when calculating electric fields from a continuous charge distribution (volumetric, surface, or line).

Azimuthal Symmetry

A type of symmetry observed in an infinite line charge where the electric field does not vary with the angle (phi component) or along the axis (z-component for a line charge along z).

Infinitely Long Line Charge Electric Field

The electric field generated by an infinitely long uniform line charge, directed radially outward if positive, inward if negative, and whose magnitude decreases with the inverse of the distance from the line.

Infinitely Large Sheet of Charge Electric Field

The electric field generated by an infinitely large uniform sheet of charge, whose magnitude is constant everywhere and whose direction is perpendicular to the sheet, pointing away if positive, or into the sheet if negative.

Electric Field Streamlines

Lines used to visualize electric fields where arrows indicate the direction of the field at every point, and the separation of the lines is inversely proportional to the strength of the field.

Equation of Streamline (Cartesian)

A differential equation used to find the path of a streamline in a Cartesian coordinate system, given by dy/dx = Ey/Ex.

Equation of Streamline (Cylindrical/Polar)

A differential equation used to find the path of a streamline in a cylindrical or polar coordinate system, given by (rho * dphi) / drho = Ephi / Erho.

Electric Field Calculation Steps

1. Find generic point (x,y,z). 2. Find coordinates of generic point charge (x',y',z'). 3. Divide charge into infinitesimal points (dQ). 4. Find distance vector (R = r - r'). 5. Find unit vector (aR = R / |R|). 6. Set up integral for dE.

Exploiting Symmetry

The practice of identifying the most convenient coordinate system (spherical, cylindrical, or Cartesian) and determining which coordinates or field components do not vary due to the problem's symmetry, simplifying electric field calculations.