Question

A charge of `-1 C` is at the origin. How much energy would be applied to or released from a `-1 C` charge if it is moved from `( -1, 3 )` to `(-2 ,7 )`?

Answer 1

`~~1.61xx10^9J`

Explanation:

Given two point charges
`"At origin"Q=-1C" and another " q =-1C`
Let the point of origin be O(0,0) where -1C charge is placed.The initial or first position of another -1C charge is A (-1,3)and its final or displaced position is B (-2.7)

The initial distance of the charge from origin O is `OA=r_i`

`r_i=sqrt((-1-0)^2+(3-0)^2)=sqrt10`

The final distance of the charge from origin O is `OB=r_f`

`r_f=sqrt((-2-0)^2+(7-0)^2)=sqrt53`

Formula for calculation PE

`PE=(U)=(kQq)/r`,
`"where "`
`k ="Coulomb'sconstant"=9xx10^9(Nm^2)/C^2`

The change in PE for movement of -1C charge from A to B is
`DeltaU=U_f-U_i=(kQq)(1/r_f-1/r_i)`
`=9xx10^9xx(-1)(-1)(1/sqrt53-1/sqrt10)J~~-1.61xx10^9J`

As the change in PE is negative the energy will be released for the movement of the charge.