OpenStax University Physics/E&M/Electric Potential

$ℰ\mathrm{\&}ℳ$ (Vol. 2):Template:Spaces 5:Electric Charges and FieldsTemplate:Spaces 6:Gauss's LawTemplate:Spaces 7:Electric PotentialTemplate:Spaces 8:CapacitanceTemplate:Spaces 9:Current and ResistanceTemplate:Spaces 10:Direct-Current CircuitsTemplate:Spaces 11:Magnetic Forces and FieldsTemplate:Spaces 12:Sources of Magnetic FieldsTemplate:Spaces 13:Electromagnetic InductionTemplate:Spaces 14:InductanceTemplate:Spaces 15:Alternating-Current CircuitsTemplate:Spaces 16:Electromagnetic Waves

Chapter 7

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For quiz at QB/d_cp2.7

Template:Colbegin $\mathrm{\Delta }{V}_{AB}=V_A-V_B=-\underset{A}{\overset{B}{\int }}\overrightarrow{E}\cdot d\overrightarrow{\ell }$ = electric potential

$\overrightarrow{E}=-\frac{\partial V}{\partial x}\hat{i}-\frac{\partial V}{\partial y}\hat{j}-\frac{\partial V}{\partial z}\hat{k}=-\overrightarrow{\mathrm{\nabla }}V$

$q\mathrm{\Delta }V$ = change in potential energy (or simply $U=qV$)

$Power=\frac{\mathrm{\Delta }U}{\mathrm{\Delta }t}=\frac{\mathrm{\Delta }q}{\mathrm{\Delta }t}V=IV=e\frac{\mathrm{\Delta }N}{\mathrm{\Delta }t}$

Electron (proton) mass = 9.11×10⁻³¹kg (1.67× 10⁻²⁷kg). Elementary charge = e = 1.602×10⁻¹⁹C.

$K=\frac{1}{2}m{v}^2$=kinetic energy. 1 eV = 1.602×10⁻¹⁹J

$V(r)=k\frac{q}{r}$ near isolated point charge

Many charges: $V_P=k\sum _1^N\frac{q_i}{r_i}\to k\int \frac{dq}{r}$. Template:Colend