ECE 106 - Electric Fields, Coordinate Systems, Coulombs Law

Electric field formula

E-> = (kQ/r^2) (r hat)

How is electric field direction determined

place a positive "test" charge

what does nonprime/prime notation mean?

prime = source

nonprime = observer

Cylindrical coordinates =

(r, φ, z)

r = projection on x-y plane

φ = angle with x-axis

z = height

Good when there is SYMMETRY about an AXIS

Spherical coordinates =

(r, φ, θ)

r = distance from origin

φ = angle with x axis

θ = angle with z axis

How to find dQ =

dQ = little bit of charge

charge density x differential element

line: ρ_l(dl)

surface: ρ_S(dS)

volume: ρ_V(dV)

differential surface element of circle =

POLAR COORDINATES

dS = rdrdφ

differential surface element of sphere =

SPHERICAL COORDINATES

dS = r²sin(θ)dθdφ

Coulombs Law

F = kq1q2/R^2

Torque on a dipole in a uniform field =

T = sF_n

s = charge separation

F_n = QEsinθ (force component normal to the dipole axis)