Physics Sheet

Potential: V(J/C )=

kQr, Potential difference ΔV= Vf-Vi = -E⋅dx . Point charge potential ΔV=V(r)-V(∞), With V(∞)=0.

Potential of several charges: add

them up. Potential is not a vector. E=-delV. Equipotential line: Work to move a charge between these points is zero so the field is conservative(can take any path) Ex: wires in a circuit. Potential energy: U (J) =qΔV. Work done by E=-ΔU. Work done against E=ΔU Energy Conservation: ΔU=-ΔEk, or Ui+Ei=Uf+Ef.

Q V(F) C>0, V=Ed.

Capacitors: C=

∂∈0, V=∂∈0d, C=∈0Ad, capacitance is dependent on geometry. Battery not

Parallel plate capacitor: E=

connected, Q cannot, and when battery is connected V cannot.

QV2=Q22C=CV22 , Energy density u=∈0E22

Energy stored in a capacitor: U=

Capacitor networks: Series: charge is the same on all capacitors, Ceq=(1/C_1 +1/C_2 +…)-1 C1+C2+...Parallel: V's are equal. Ceq =C1+C2+...

dqdt=free charge density ×volume rate of flow=nqvDA, q=IΔt. Microscopic current: Volume rate IA,(A/m^2) E=Jρ,

Current:I=

of flow = vDA, vD is drift velocity. nq= free charge density, q= charge of carriers, n=density of free charge carriers. Current Density J=

ρ= resistivity. Resistance: (Ω)=

ρLA. Ohms law: V=IR. Resistors in Series: R

tot

1R1+1R2+…)-1

=R1+R2..., Resistors in Parallel Rtot=(

=Batteries: Non ideal: "open circuit terminal voltage" is ε, because there is no current. ε-Ir=IR Power: IV=I2R=V2/R=change in energy over time. Kirchoff's laws: ΣI's at a junction=0, ΣV's in a loop=0. I in +, I out -. Thats voltage changes. RC circuits: