Question

A charge of `-2 C` is at the origin. How much energy would be applied to or released from a `4 C` charge if it is moved from `(-7 ,1 )` to `(4 ,-6 )`?

Answer 1

`197` `MJ` of energy is released.

Explanation:

Electrostatic Potential Energy: The electrostatic potential energy of a charge pair `Q` and `q` separated by a distance `r` is :

`U(r) = -k(Qq)/r; \qquad k \equiv 1/(4\pi\epsilon_0) = 8.99\times10^9 (N.m^2)/C^2`

Assuming that the units of the coordinates are in meters.
`r_i = \sqrt{(-7m)^2+(1m)^2} = \sqrt{50}` `m = 7.071` `m`
`r_f = \sqrt{(4m)^2+(-6m)^2} = 7.211` `m`

`\Delta U = U_f - U_i = -kQq(1/r_f - 1/r_i)`
`= -(8.99\times10^9 (Nm^2)/C^2)(-2C)(4C)(1/(7.211m) - 1/(7.071m))`

`= - 197` `MJ`

Change in potential energy is negative. This means the potential energy has decreased. So the energy is released.