Consider a capacitor made of two square plates of side 'l' . The distance between the two plates is 'd'.
a) We insert a dielectric of dielectric constant K>1 and width l, a distance x (as in the diagram). What is the total capacitance of this arrangement? Express your answer in terms of the following variables and constants, if relevant, l, x, d, K and epsilon _0 (enter epsilon_0 for epsilon _0).
b) The capacitor is now connected to battery which provides a difference of potential V_0 across the capacitor. What is the energy stored in the capacitor?
Express your answer in terms of the following variables, if relevant, l, x, d, K,V_0 and epsilon _0 (enter epsilon_0 for \epsilon _0 and V_0 for V_0).
c)While the battery is still connected to the capacitor, we now move the dielectric slab a bit further in between the plates, increasing x by an amount Delta. What is the change in the energy stored in the capacitor?
Express your answer in terms of the following variables, if relevant, l, x, d, K, V_0,Delta and epsilon _0 (enter epsilon_0 for epsilon _0 , Delta for Delta and V_0 for V_0).
d) What is the work done by the battery while we push the dielectric slab in from its original position x to x+Delta? (make sure you have the correct sign!) Express your answer in terms of the following variables, if relevant, l, x, d ,K, V_0, Delta and epsilon _0 (enter epsilon_0 for epsilon _0 , Delta for Delta and V_0 for V_0).
e) What is the work done by us while we push the dielectric slab in? (make sure you have the correct sign!) Express your answer in terms of the following variables, if relevant, l, x, d, K, V_0, Delta and epsilon _0 (enter epsilon_0 for epsilon _0 , Delta for Delta and V_0 for V_0).
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