Answer :
Answer:
[tex]\displaystyle \frac{U}{U_o}=\frac{1}{2}[/tex]
Explanation:
Energy Stored in Capacitors
The capacitance of a parallel-plate capacitor is given by
[tex]\displaystyle C=\epsilon_0\frac{A}{d}[/tex]
Where [tex]\epsilon_o[/tex] is the permitivity of the dielectric, A is the area of the plates and d is their separation. If the separation was doubled, the new capacitance would be
[tex]\displaystyle C'=\epsilon_0\frac{A}{2d}=\frac{C}{2}[/tex]
The energy stored in the initial condition is
[tex]\displaystyle U_o=\frac{CV^2}{2}[/tex]
And the energy stored when the separation doubles is
[tex]\displaystyle U=\frac{CV^2}{4}[/tex]
Thus the ratio
[tex]\displaystyle \frac{U}{U_o}=\frac{\frac{CV^2}{4}}{\frac{CV^2}{2}}=\frac{1}{2}[/tex]
[tex]\boxed{\displaystyle \frac{U}{U_o}=\frac{1}{2}}[/tex]
The energy is half the initial energy