A charge of #-1 C# is at the origin. How much energy would be applied to or released from a # 6 C# charge if it is moved from # (-3, 1 ) # to #(4 ,4 ) #?

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Answer 1 · 2018-02-21T07:51:59

The energy released is #=7.53*10^9J#

The potential energy is

#U=k(q_1q_2)/r#

The charge #q_1=-1C#

The charge #q_2=6C#

The Coulomb's constant is #k=9*10^9Nm^2C^-2#

The distance

#r_1=sqrt((-3)^2+(1)^2)=sqrt10m#

The distance

#r_2=sqrt((4)^2+(4)^2)=sqrt(32)#

Therefore,

#U_1=k(q_1q_2)/r_1#

#U_2=k(q_1q_2)/r_2#

#DeltaU=U_2-U_1=k(q_1q_2)/r_2-k(q_1q_2)/r_1#

#=k(q_1q_2)(1/r_1-1/r_2)#

#=9*10^9*((-1)*(6))(1/sqrt32-1/(sqrt10))#

#=7.53*10^9J#

The energy released is #=7.53*10^9J#