E for an infinite charged plate:

E=

=σ/(2ε₀)

Capacitence of parallel plate capacitor:

C=

=ε₀A/d

Torque on a loop of wire in a magnetic field:

τ_loop=

=IA x B

E between parallel plates:

E=

=σ/ε₀

B for infinitely long wire:

B=

=1/(4πa) *μ₀I

E for spherical distribution, r>a:

E_sphere=

=kQ/r²

Voltage induced in a coil:

V=

=-NBAcosθ

E for infinite cylinder, r>a:

E_cylinder=

=2kλ/r

E for a spherical distribution, r<a:

E_sphere=

=kQr/a³

B for a solenoid:

B=

=μ₀nI

(n= number of loops / unit length)

E for infinite cylinder, r<a:

E_cylinder=

=2kλr/a²

Inductance for a solenoid:

L_solenoid=

=μ₀n²V

B for a toroid:

B_toroid=

=μ₀NI/(2πr)

(N= total number of loops)

Electric potential energy:

ΔU_e=

=-q∫E ·ds 

=qV

=W

Voltage across resistor:

ΔV=

=IR

Potential difference:

ΔV=

=-∫E ·ds

=EΔx

=kq/r

Angular frequency:

ω=

=2πf

Tangential component is continuous

Normal component is discontinuous iff σ≠0

Lorentz force:

F=

=q(E+v x B)

Natural frequency for an LC circuit:

ω₀=

=1/√(LC)

Capacitence:

C=

=Q/ΔV

Parallel circuit:

ΔV_T=

Q_T=

C_eq=

R_T=

ΔV₁=ΔV₂=...

=Q₁+Q₂+...

=C₁+C₂+...

1/R_T=1/R₁+1/R₂+...

Electrical Work:

W=

=ΔQΔV

Average Power from E and B:

P_avg=

=S_avgA

∫B · ds =

(closed integral)

=μ₀I

D Field:

D=

H Field:

H=

=εE

=B/μ

Inductance Definition:

L=

=NΦ/I

(Φ = flux)

Torque on dipole in E field:

τ=

=p x E

(p = electric dipole moment = qd)

del · D = ρ_f

del x E = - ∂B/∂t

del · B = 0

del x H = J_f + ∂D/∂t

Induced motional EMF:

V_motion=

Motional E Field:

E_motion=

=Bvl

=v x B

Current Density:

J=

=σE

=nqv_d

=ρv

(n= charge-carrier density)

Electrical Power:

P=

=IΔV

Wave number:

k=

=2π/λ

E=

=k∫dq/r²

Series Circuit:

Q_T=

ΔV_T=

C_eq=

R=

=Q₁=Q₂=...

=ΔV₁+ΔV₂+...

1/C_eq=1/C₁+1/C₂+...

=R₁+R₂+...

Total energy density:

u=

u_avg=

=u_E+u_B

=B²/μ₀

=ε₀E²

=½ε₀E_max²

=B²/(2μ₀)

Average Poynting vector:

S_avg=

=I

=E_maxB_max/(2μ₀)

=cu_avg

Pressure from EM wave:

P_reflect=

P_absorb=

=2S/c

=S/c

Magnetic Flux:

Φ_B=

=∫B · dA

=(closed)∫B · dA =0

Poynting Vector:

S=

=1/μ₀ E x B

=E²/(μ₀c)

=cB²/μ₀

self-induced EMF:

E_L=

=-L dI/dt

Energy stored in a capacitor:

U=

=Q²/(2C)

=½ QΔV

=½CΔV²

∫E·ds=

=-dΦ_B/dt

c

1/√(μ₀ε₀)

E_t=0

B_n=0