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Chapter 24: Problem 9

A parallel plate capacitor is connected to a battery for charging. After some time, while the battery is still connected to the capacitor, the distance between the capacitor plates is doubled. Which of the following is (are) true? a) The electric field between the plates is halved. b) The potential difference of the battery is halved. c) The capacitance doubles. d) The potential difference across the plates does not change. e) The charge on the plates does not change.

Short Answer

Expert verified
(Select all that apply.) a) The electric field between the plates is halved. b) The potential difference of the battery is halved. c) The capacitance doubles. d) The potential difference across the plates does not change. e) The charge on the plates does not change. Answer: a) The electric field between the plates is halved, d) The potential difference across the plates does not change, and e) The charge on the plates does not change are true statements.

Step by step solution

01

a) The electric field between the plates is halved

After doubling the distance, we can use the electric field formula to find out how the electric field changes: E_new = V/(2d), which is equal to (1/2) * V/d. This shows that the electric field (E_new) is indeed halved as compared to the initial electric field (E).
02

b) The potential difference of the battery is halved

The potential difference across the battery remains constant as it is not affected by the change in distance between the plates. Therefore, this statement is false.
03

c) The capacitance doubles

Using the capacitance formula for a parallel plate capacitor, we can see how the capacitance changes when the distance between the plates is doubled: C_new = ε₀ * A/(2d). This is equal to (1/2) * ε₀ * A/d which is half of the initial capacitance, not double. So, this statement is false.
04

d) The potential difference across the plates does not change

As the capacitor is still connected to the battery, the potential difference across the plates remains the same as it is equal to the potential difference of the battery. Therefore, this statement is true.
05

e) The charge on the plates does not change

As the potential difference remains the same and the charge formula is Q = CV, since we found out that C is halved, and V remains constant, the charge on the plates will also not change. Therefore, this statement is true. In conclusion, statements a), d), and e) are true, while statements b) and c) are false.

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Most popular questions from this chapter

The Earth can be thought of as a spherical capacitor. If the net charge on the Earth is \(-7.8 \cdot 10^{5} \mathrm{C},\) find \((\) a) the capacitance of the Earth and (b) the electric potential energy stored on the Earth's surface

A quantum mechanical device known as the Josephson junction consists of two overlapping layers of superconducting metal (for example, aluminum at \(1.00 \mathrm{~K}\) ) separated by \(20.0 \mathrm{nm}\) of aluminum oxide, which has a dielectric constant of \(9.1 .\) If this device has an area of \(100 . \mu \mathrm{m}^{2}\) and a parallel plate configuration, estimate its capacitance.

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