A charge of #-1 C# is at the origin. How much energy would be applied to or released from a # -1 C# charge if it is moved from # ( -1, 3 ) # to #(-2 ,7 ) #?

1 Answer
Jul 3, 2016

Answer:

#~~1.61xx10^9J#

Explanation:

Given two point charges
#"At origin"Q=-1C" and another " q =-1C#
Let the point of origin be O(0,0) where -1C charge is placed.The initial or first position of another -1C charge is A (-1,3)and its final or displaced position is B (-2.7)

The initial distance of the charge from origin O is #OA=r_i#

#r_i=sqrt((-1-0)^2+(3-0)^2)=sqrt10#

The final distance of the charge from origin O is #OB=r_f#

#r_f=sqrt((-2-0)^2+(7-0)^2)=sqrt53#

Formula for calculation PE

#PE=(U)=(kQq)/r#,
#"where " #
#k ="Coulomb'sconstant"=9xx10^9(Nm^2)/C^2#

The change in PE for movement of -1C charge from A to B is
#DeltaU=U_f-U_i=(kQq)(1/r_f-1/r_i)#
#=9xx10^9xx(-1)(-1)(1/sqrt53-1/sqrt10)J~~-1.61xx10^9J#

As the change in PE is negative the energy will be released for the movement of the charge.