ch 5 extended electric fields L4 and L5

see slides for the derivations, good way of thinking

dq =

λdl for 1D, σdA for 2D, ρDV for 3D, where greek letters are the charge density

electric field on middle axis of 1d uniform line charge

E(z) = 1/4πε₀ * λL/z√z² + L²/4 in direction of k hat

when z → infinity, the result reduces to

1/4πε₀ * q/z² in direction of k hat ; essentially reduces to a point charge

e field of a ring of charge

1/4πε₀ * q_totz/(R² + z²)^3/2

e field of a charged disk

E_z = σ/2ε₀ (1 - z/√z² + R²)

electric field near a very large 2D charged sheet is

a constant proportional to the charge density (E_z = σ/2ε₀)

in between a parallel plate capacitor, the fields

add up

outside a parallel plate capacitor, the fields

cancel each other

characteristics of field lines

start at + and end at -, stronger E-field if closer together, E points along the tangent of the field line at any points, coulomb force on test charge Q is along this tangent