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Chapter 24: Problem 23

A parallel plate capacitor is constructed from two plates of different areas. If this capacitor is initially uncharged and then connected to a battery, how will the amount of charge on the big plate compare to the amount of charge on the small plate?

Short Answer

Expert verified
Answer: The charges on the big and small plates of a parallel plate capacitor will be equal and opposite, irrespective of the sizes of the plates, because of the homogenous electric field between them and charge conservation in a closed circuit.

Step by step solution

01

Understanding the Capacitor

A parallel plate capacitor consists of two conducting plates separated by a distance. When connected to a battery, one plate gains positive charge, and the other plate gains an equal amount of negative charge. The charges on both plates will be equal and opposite.
02

Charging Process

When the parallel plate capacitor is connected to a battery, the battery provides positive charges to one plate and takes away an equal amount of charges from the other plate, making it negatively charged. This process continues until the potential difference across the plates becomes equal to the battery's EMF.
03

Amount of Charge on Plates

In the given exercise, the capacitor has two plates with different areas. However, charges will still distribute uniformly on both plates as the electric field between them is homogenous. Therefore, the charges on both plates will be equal and opposite, keeping in mind that the total charges on the connected components in a closed circuit remain conserved.
04

Conclusion

The charges on the big and small plates of a parallel plate capacitor will be equal and opposite, irrespective of the sizes of the plates, because of the homogenous electric field between them and charge conservation in a closed circuit.

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Most popular questions from this chapter

Must a capacitor's plates be made of conducting material? What would happen if two insulating plates were used instead of conducting plates?

The Earth is held together by its own gravity. But it is also a charge-bearing conductor. a) The Earth can be regarded as a conducting sphere of radius \(6371 \mathrm{~km},\) with electric field \(\vec{E}=(-150 . \mathrm{V} / \mathrm{m}) \hat{r}\) at its surface, where \(\hat{r}\) is a unit vector directed radially outward. Calculate the total electrostatic potential energy associated with the Earth's electric charge and field. b) The Earth has gravitational potential energy, akin to the electrostatic potential energy. Calculate this energy, treating the Earth as a uniform solid sphere. (Hint: \(d U=-(G m / r) d m\). c) Use the results of parts (a) and (b) to address this question: To what extent do electrostatic forces affect the structure of the Earth?

A parallel plate capacitor with a plate area of \(12.0 \mathrm{~cm}^{2}\) and air in the space between the plates, which are separated by \(1.50 \mathrm{~mm},\) is connected to a \(9.00-\mathrm{V}\) battery. If the plates are pulled back so that the separation increases to \(2.75 \mathrm{~mm}\) how much work is done?

An \(8.00-\mu F\) capacitor is fully charged by a \(240 .-V\) battery, which is then disconnected. Next, the capacitor is connected to an initially uncharged capacitor of capacitance \(C,\) and the potential difference across it is found to be \(80.0 \mathrm{~V}\) What is \(C ?\) How much energy ends up being stored in the second capacitor?

Does it take more work to separate the plates of a charged parallel plate capacitor while it remains connected to the charging battery or after it has been disconnected from the charging battery?
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