Spring 2010 Solutions - FSU Physics Department

and becauseQ=CV, this can also be writtenF2 2CV=−2εA0(b) Assume now that a glass plate of the same area A completely fills the spacebetween the plates. The glass has a dielectric constant κ. How much work isrequired to pull the glass plate out of the capacitor?When a glass plate is inserted between the two capacitor plates, thecapacitance and the potential between the plates will change(although the total charge will remain the same.) This will causethe Energy stored on the plates to also change.When the glass plate is between the capacitor plates:C'A= κε0zQV' = C'Without the glass plate between the capacitor plates:CThis means thatVV'VV'A= ε0zQV= CQ Q C' A A= ⎛ ⎜ ⎞ ⎟ ⎛ ⎜ ⎞ ⎟= =⎛ ⎜κε⎞ ⎛ 0 ⎟ ⎜ε⎞0 ⎟⎝C ⎠ ⎝C' ⎠ C ⎝ z ⎠ ⎝ z ⎠= κThe energy stored in the capacitor when the glass is between theplates is given by2 22Q Q z Q1 1 1W'i= = =2 C' 2κεA κ 2CAnd without the glass plateWf2 2 2Q Q z Q= 1 12 C= 2 ε A= 2CThe energy required to remove the glass plate isW= W −Wreq.f i002Q ⎛ 1 ⎞= ⎜1−⎟2C⎝ κ ⎠