Respuesta :
The total work done of 0.018 joules is needed to move the charges apart and double the distance between them.
We have two electric charges q(A) = 1μc and q(B) = -2μc kept at a distance 0.5 meter apart.
We have to calculate much work is needed to move the charges apart and double the distance between them.
What s the formula to calculate the Potential Energy of a system of two charges (say 'q' and 'Q') separated by a distance 'r' ?
The potential energy of the system of two charges separated by a distance is given by -
[tex]U = \frac{1}{4\pi\epsilon_{o} } \frac{qQ}{r}[/tex]
In order to solve this question, it is important to remember the work - energy theorem which states -
"The change in the energy of the body is equal to work done on it"
Hence, using this work -energy theorem in the question given to us we get -
[tex]U_{f} -U_{i} =W_{net}[/tex]
In our case -
[tex]U_{f} = \frac{1}{4\pi\epsilon_{o} } \frac{qQ}{2r}\\\\U_{i} = \frac{1}{4\pi\epsilon_{o} } \frac{qQ}{r}\\\\W=\frac{1}{4\pi\epsilon_{o} } \frac{qQ}{2r} - \frac{1}{4\pi\epsilon_{o} } \frac{qQ}{r}\\\\W = \frac{qQ}{4\pi\epsilon_{o}r} (\frac{1}{2} -1)\\\\W = 9\times 10^{9}\times \frac{1 \times 10^{-6} \times 2\times10^{-6} }{0.5} \times \frac{-1}{2}[/tex]
W = 0.018 joules
Hence, the total work done should be 0.018 joules.
To solve more question on potential energy, visit the link below -
https://brainly.com/question/15014856
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