A charge of 7 C is at the origin. How much energy would be applied to or released from a  9 C charge if it is moved from  (2 ,-2 )  to (2 ,-1 ) ?

Jun 24, 2018

$335.66 \cdot {10}^{9} J$ of energy is relesed

Explanation:

As energy is scalar, only the distance of charges from origin are considered.

${U}_{i} = \frac{1}{4 \pi {\epsilon}_{0}} \frac{7 \cdot 9}{\sqrt{8}}$

and

${U}_{f} = \frac{1}{4 \pi {\epsilon}_{0}} \frac{7 \cdot 9}{\sqrt{5}}$

$\text{Work done by external force} = {U}_{f} - {U}_{i}$

$\Rightarrow \text{Work done by external force} = \frac{1}{4 \pi {\epsilon}_{0}} \frac{7 \cdot 9}{\sqrt{5}} - \frac{1}{4 \pi {\epsilon}_{0}} \frac{7 \cdot 9}{\sqrt{8}}$

$\Rightarrow \text{Work done by external force"="Energy released/gained} = - 335.66 \cdot {10}^{9} J$

As work done is negetive, energy is released.