Question

A charge of `-1 C` is at the origin. How much energy would be applied to or released from a `6 C` charge if it is moved from `(-3, 1 )` to `(2 ,-1 )`?

Answer 1

`W=E_p=-54*10^9((sqrt10+sqrt5)/sqrt50)" "J`

Explanation:

`q_1=-1C" "q_2=6C`
`r_1:"distance between origin and the point of (-3,1)"`
`r_1=sqrt((-3-0)^2+(1-0)^2)=sqrt((-3)^2+1^2)=sqrt 10`
`r_2:"distance between origin and the point of (2,-1)"`
`r_2=sqrt((2-0)^2+(-1-0)^2)=sqrt(2^2+(-1)^2)=sqrt5`

`W=E_p=(k*q_1*q_2)/r_1+(k*q_1*q_2)/r_2`

`W=E_p=k*q_1*q_2(1/r_1+1/r_2)`

`W=E_p=k*q_1*q_2((r_1+r_2)/(r_1*r_2))`

`W=E_p=9*10^9*(-1)*6((sqrt10+sqrt5)/(sqrt10*sqrt5))`

`W=E_p=-54*10^9((sqrt10+sqrt5)/sqrt50)" "J`
`"The energy of system has decreased"`