# A charge of #5 C# is at the origin. How much energy would be applied to or released from a # -2 C# charge if it is moved from # ( 3 , 6 ) # to #( -3 , 5) #?

##### 1 Answer

The potential energy of the -2 C charge changes from

#### Explanation:

Fortunately, by doing this problem using energy methods, we need only calculate the energy at the initial and final locations, and do not have to consider the (challenging) task of evaluating the force at each point along the path. (Calculus, anyone?)

At (3,6), the distance between the charges is

By Coulomb's law, the force is

and the potential energy is

At (3,-5) the distance between the charges is

By Coulomb's law, the force is

and the potential energy is

Thus, the change in energy has been

(As an aside, in all the above, the location of zero potential energy is taken to be at