↦ q 1 = 7 μ C ( − 9 , 0 , 0 ) r , ( 0 , 0 , 0 ) r ( 9 , 0 , 0 ) q 2 = − 2 μ C \underset{(-9,0,0)}{\stackrel{\mathrm{q}_{1}=7 \mu \mathrm{C}}{\mapsto}} \mathrm{r} \underset{(0,0,0)}{,} \underset{(9,0,0)}{r} \mathrm{q}_{2}=-2 \mu \mathrm{C} ( − 9 , 0 , 0 ) ↦ q 1 = 7 μ C r ( 0 , 0 , 0 ) , ( 9 , 0 , 0 ) r q 2 = − 2 μ C d V = − E → ⋅ d r → \mathrm{dV}=-\overrightarrow{\mathrm{E}} \cdot \overrightarrow{\mathrm{dr}} dV = − E ⋅ dr ∫ 0 v d V = − ∫ ∞ r A r 2 d r \int_{0}^{\mathrm{v}} \mathrm{dV}=-\int_{\infty}^{\mathrm{r}} \frac{\mathrm{A}}{\mathrm{r}^{2}} \mathrm{dr} ∫ 0 v dV = − ∫ ∞ r r 2 A dr V = − [ − A r 2 ] ∞ r ⇒ V = A r \mathrm{V}=-\left[\frac{-\mathrm{A}}{\mathrm{r}^{2}}\right]_{\infty}^{\mathrm{r}} \Rightarrow \mathrm{V}=\frac{\mathrm{A}}{\mathrm{r}} V = − [ r 2 − A ] ∞ r ⇒ V = r A U = U self + U interaction \mathrm{U}=\mathrm{U}_{\text {self }}+\mathrm{U}_{\text {interaction }} U = U self + U interaction = q 1 v 1 = q 2 v 2 + k q 1 q 2 2 r =\mathrm{q}_{1} \mathrm{v}_{1}=\mathrm{q}_{2} \mathrm{v}_{2}+\frac{\mathrm{kq}_{1} \mathrm{q}_{2}}{2 \mathrm{r}} = q 1 v 1 = q 2 v 2 + 2 r kq 1 q 2 = 7 × 10 − 6 A 9 × 10 − 2 − 2 × 10 − 6 A 9 × 10 − 2 =7 \times 10^{-6} \frac{\mathrm{~A}}{9 \times 10^{-2}}-2 \times 10^{-6} \frac{\mathrm{~A}}{9 \times 10^{-2}} = 7 × 1 0 − 6 9 × 1 0 − 2 A − 2 × 1 0 − 6 9 × 1 0 − 2 A − 9 × 10 9 × 14 × 10 − 12 2 × 9 × 10 − 2 -\frac{9 \times 10^{9} \times 14 \times 10^{-12}}{2 \times 9 \times 10^{-2}} − 2 × 9 × 1 0 − 2 9 × 1 0 9 × 14 × 1 0 − 12 = 5 × 10 − 6 × 9 × 10 5 9 × 10 − 2 − 7 × 10 − 1 =\frac{5 \times 10^{-6} \times 9 \times 10^{5}}{9 \times 10^{-2}}-7 \times 10^{-1} = 9 × 1 0 − 2 5 × 1 0 − 6 × 9 × 1 0 5 − 7 × 1 0 − 1 = 50 − 0.7 =50-0.7 = 50 − 0.7 = 49.3 J =49.3 \mathrm{~J} = 49.3 J
