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 # (-5 ,3 ) # to #(3 ,-4 ) #?

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Answer 1 · 2018-01-12T13:40:26

The energy released is #=2.052*10^9J#

The potential energy is

#U=k(q_1q_2)/r#

The charge #q_1=-2C#

The charge #q_2=4C#

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

The distance

#r_1=sqrt((-5)^2+(3)^2)=sqrt(34)m#

The distance

#r_2=sqrt((3)^2+(-4)^2)=sqrt(25)=5m#

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*((-2)*(4))(1/5-1/sqrt(34))#

#=-2.052*10^9J#