Question

Two 13-cm-diameter electrodes 0.56 cm apart form a parallel-plate capacitor. The electrodes are attached by metal wires to the terminals of a 11 Vbattery. After a long time, the capacitor is disconnected from the battery but is not discharged. What are the 1-----

a) charge on each electrode, b) the electric field strength inside the capacitor, and c) the potential difference between the electrodes right after the battery is disconnected?

2-----

What are a) the charge on each electrode, b) the electric field strength inside the capacitor, and c) the potential difference between the electrodes after insulating handles are used to pull the electrodes away from each other until they are 1.1 cm apart?

3-------

What are a) the charge on each electrode, b) the electric field strength inside the capacitor, and c) the potential difference between the electrodes after the original electrodes (not the modified electrodes of parts D-F) are expanded until they are 26 cm in diameter?

Answer 1

The data

Part 1

The electric field between the parallel plate capacitor is constant and (the magnitude) is given by

the above electric field (is the electric field inside the capacitor) is also given by

,

where is the charge density, hence

the charge on each electrode is equal but the opposite sign and is given by

the potential difference between the electrodes right after the battery is disconected is 11.0 v.

Part 2

If we used insulating handles to pull the electrodes away, the charge remains unchanged so

a) on the positive electrode

and on the negative electrode

The electric field inside the capacitor also remains unchanged, because

the potential difference between the electrodes is now given by

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Part 3

a) in this case the charge also remains unchanged

a) on the positive electrode

and on the negative electrode

b) but the electric field is now smaller than the precedent case, because the area of the plates is now larger,

now as the new diameter is twice the precedent, the new electric field is

c) the potential difference is now given by

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