Ch. 2 Electrostatics

force of gravity formula

gravitational constant: 6.67 × 10^-11 Nm²/kg²

coulomb’s law

k=9.0 × 10^9 NR²/C²

r-r’

Electric Field of a Point Charge

Force of a Charge

Fq=qE

Electric Fields of Continuous Distributions

Electric Flux Formula

Gaussian Surface

Gauss’s Law

∇⋅E=ρ/ε₀

Insulating & Conducting Surfaces

Qenc=σA

Insulating Surface: σ/2ε₀

Conducting Surface: σ/ε₀

Electric Potential

V(xo)-V(xa)=kQ/rb-kQ/ra)=-∫(xa→xb) E⋅dl

• as long as xa/=xb, then this formula is path independent

• if xa=xb, then E⋅dl = 0

• ∇x E =0, the curl of an electric field vanishes when it is a possible electric field

Electric Potential due to a Point Charge

V=kQ/r

Electric Field & Electric Potential Relation

E=-∇V

Volt → Energy Conversion

1 Volt = 1 Joule/Coulomb

Electric Potential due to Continuous Distribution

Work due to Electric Potential

W=qV

sum of charge distribution

W=Q²/8πε₀²R=1/2∫ρVdτ

U=(ε₀/2)E²

Laplacian of Electric Potential

∇²V=ρ/ε₀

Relationship between Electric Field, Electric Charge, and Electric Potential

E=-∇V=k∫ρ(r’)/(r-r’)dτ

V=-∫E⋅dl=k∫ρ(r’)/(r-r’)dτ

ρ=-ε₀∇²V=ε₀(∇⋅E)

Capacitors

Q=CV

C=ε₀A/d