# A charge of #2 C# is at the origin. How much energy would be applied to or released from a # 1 C# charge if it is moved from # ( -4, 3 ) # to #( 1 , 4 ) #?

##### 1 Answer

This energy is applied

#### Explanation:

First we need to find the distances from the origin to the 1C charge at both points.

I'm assuming all distance measurements are in meters

The first observation you should make is that the 1C charge is being moved *closer* to the 2C charge, an action that, because of their repulsion, requires energy to be applied.

Let's start from our given: Coulomb's Law

Where

From here, you can find the voltage (potential energy) at each point by substituting

Simplifying

Where

We also know that work is, in this problem, equal to the change in voltage (potential energy):

Simplifying

From here, we can just put in the numbers:

One Coulomb is a huge amount of charge; normally you would work problems with nothing larger than micro Coulombs.