Answer: (2) > (1) > (3) > (4)
Explanation:
(1) a +1 charge and a -1 charge separated by 200 pm:
The potential energy in this case will be,
[tex]U_E & = k\;\rm (N\cdot m^2/C^2) \dfrac{(+1 \ C)(-1 \ C)}{200 \times 10^{-9} \ m } \\ & = - \frac{1}{2}k \times 10^7 \ \rm J[/tex]
(2) a +1 charge and a +1 charge separated by 100 pm:
The potential energy in this case will be,
[tex]U_E & = k\;\rm (N\cdot m^2/C^2) \dfrac{(+1 \ C)(+1\ C)}{100 \times 10^{-9} \ m } \\ & = k \times 10^7 \ \rm J[/tex]
(3) a +1 charge and a -1 charge separated by 100 pm:
The potential energy in this case will be,
[tex]U_E & = k\;\rm (N\cdot m^2/C^2) \dfrac{(+1 \ C)(-1 \ C)}{100 \times 10^{-9} \ m } \\ & = - k \times 10^7 \ \rm J[/tex]
(4) a +2 charge and a -1 charge separated by 100 pm:
The potential energy in this case will be,
[tex]U_E & = k\;\rm (N\cdot m^2/C^2) \dfrac{(+2 \ C)(-1 \ C)}{100 \times 10^{-9} \ m } \\ & = - 2k \times 10^7 \ \rm J[/tex]
So, the order from highest potential energy to lowest potential energy is:
(2) > (1) > (3) > (4)