# A charge of 3 C is at the origin. How much energy would be applied to or released from a  -1 C charge if it is moved from  ( 2 , -8 )  to (-2 , 5 ) ?

Mar 14, 2016

$W \cong - 8 , 37 \cdot {10}^{9} J$

#### Explanation:

${P}_{1} \left(2 , - 8\right) \text{ } {P}_{2} = \left(- 2 , 5\right)$
${r}_{1} = \sqrt{{\left(2 - 0\right)}^{2} + {\left(- 8 - 0\right)}^{2}} = \sqrt{4 + 64} = \sqrt{68}$
"(distance between origin and the point of " P_1)

${r}_{2} = \sqrt{{\left(- 2 - 0\right)}^{2} + {\left(5 - 0\right)}^{2}} = \sqrt{4 + 25} = \sqrt{29}$
"(distance between origin and the point of " P_2)

$E = k \frac{{q}_{1} \cdot {q}_{2}}{r} _ 1 + k \frac{{q}_{1} \cdot {q}_{2}}{r} _ 2 \text{ (1)}$
$\text{it is done work; if a charge is moved from one point to another.}$
$\text{Work doing by system is equal the potential energy of system.}$
$\text{We obtain the fallowing equation; if we rearrange the equation (1)}$
$W = k . {q}_{1} \cdot {q}_{2} \left(\frac{1}{r} _ 1 + \frac{1}{r} _ 2\right)$
$W = k \cdot 3 \cdot \left(- 1\right) \left(\frac{1}{\sqrt{68}} + \frac{1}{\sqrt{29}}\right)$
$W = - 3 k \left(\frac{\sqrt{29} + \sqrt{68}}{\sqrt{68 \cdot 29}}\right) \text{ } k = {9.10}^{9}$
$W = - 27 \cdot {10}^{9} \cdot 0 , 31$
$W \cong - 8 , 37 \cdot {10}^{9} J$
$\text{The energy of system has decreased}$