A charge of #7# #C# is at the origin. How much energy would be applied to or released from a # 5# # C# charge if it is moved from # (-5, 1 ) # to #(2 ,-1 ) #?

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Answer 1 · 2017-06-24T13:27:17

The potential energy difference between the initial and final positions of the charges will be #8.2xx10^10# #J#.

We care only about the distance between the two charges. We can use Pythagoras' theorem to calculate the distances and the change:

#r_"initial"=sqrt((-5^2)+1^2)=sqrt(25+1)=sqrt(26)=5.1# #m# (we have to assume the units are #m#, although we were not told)

#r_"final"=sqrt(2^2+(-1)^2)=sqrt(4+1)=sqrt(5)=2.2# #m#

Since both charges are positive, and they are moved closer together, electric potential energy will be added to the system.

#E_"initial"=(kq_1q_2)/r=(9xx10^9xx7xx5)/5.1=6.1xx10^10# #J#

#E_"final"=(kq_1q_2)/r=(9xx10^9xx7xx5)/2.2=1.2xx10^11# #J#

#E_"change"=E_"final"-E_"initial"#
#=1.4xx10^11-6.1xx10^10=8.2xx10^10# #J#