E4πr2 = ρ(4πr3/3)/ε0
Rules for drawing field lines and equipotential lines
Gauss' law, the principle of superposition:
Field due to the sphere at P Ex = (1(/4πε0))σ4πR2/(2R)2
= σ/(4ε0), Ey = Ez = 0.
Field due to the plane at P Ez = σ/(2ε0), Ey = Ex = 0.
E2 = Ex2 + Ey2. E = (√5/4) σ/ε0.
The principle of superposition, the electric field and potential of a point charge
Motion of charges in a uniform magnetic field
Ohms law, V = IR
R = ρ1L1/A1 + ρ2L2/A2
Ampere's law, the Biot-Savart law
B near the surface is given by Bs = μ0I/(2πr) where r = 10-3
m (from Ampere's law).
B at the center of the ring is given by Bc = μ0I/(2R), where R = 10-1 m
(from the Biot-Savart law, dB(r) = (μ0/4π)[Idl×(r-r')/|r-r'|3]). Bs/Bc = 100/π.
Force between current-carrying wires, right-hand rule
emf = ΔΦB/∆t = A ΔB/∆t
V = V0[1 - exp(-(t-t0)/(RC))]