University Physics Volume 2

# Key Equations

### Key Equations

 Capacitance $C=QVC=QV$ Capacitance of a parallel-plate capacitor $C=ε0AdC=ε0Ad$ Capacitance of a vacuum spherical capacitor $C=4πε0R1R2R2−R1C=4πε0R1R2R2−R1$ Capacitance of a vacuum cylindrical capacitor $C=2πε0lln(R2/R1)C=2πε0lln(R2/R1)$ Capacitance of a series combination $1CS=1C1+1C2+1C3+⋯1CS=1C1+1C2+1C3+⋯$ Capacitance of a parallel combination $CP=C1+C2+C3+⋯CP=C1+C2+C3+⋯$ Energy density $uE=12ε0E2uE=12ε0E2$ Energy stored in a capacitor $UC=12V2C=12Q2C=12QVUC=12V2C=12Q2C=12QV$ Capacitance of a capacitor with dielectric $C=κC0C=κC0$ Energy stored in an isolated capacitor withdielectric $U=1κU0U=1κU0$ Dielectric constant $κ=E0Eκ=E0E$ Induced electrical field in a dielectric $E→i=(1κ−1)E→0E→i=(1κ−1)E→0$