OpenStax University Physics/E&M/Electric Potential

For quiz at QB/d_cp2.7
$$\Delta V_{AB}=V_A-V_B=-\int_A^B\vec E\cdot d\vec\ell$$ = electric potential

$$\vec E=-\tfrac{\partial V}{\partial x}\hat i- \tfrac{\partial V}{\partial y}\hat j -\tfrac{\partial V}{\partial z}\hat k = -\vec\nabla V$$

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

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

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

$$K=\tfrac 1 2 mv^2 $$=kinetic energy. 1 eV = 1.602×10−19J

$$V(r)=k\tfrac q r$$ near isolated point charge

Many charges: $$V_P=k\sum_1^N \frac{q_i}{r_i} \to k\int\frac{dq}{r}$$.