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Chapter 21: Problem 9

A metal plate is connected by a conductor to a ground through a switch. The switch is initially closed. A charge \(+Q\) is brought close to the plate without touching it, and then the switch is opened. After the switch is opened, the charge \(+Q\) is removed. What is the charge on the plate then? a) The plate is uncharged. b) The plate is positively charged. c) The plate is negatively charged. d) The plate could be either positively or negatively charged, depending on the charge it had before \(+Q\) was brought near.

Short Answer

Expert verified
Answer: The plate is negatively charged.

Step by step solution

01

Analyze the situation when the switch is closed and +Q is brought near the plate

When the switch is closed, the plate is connected to the ground, allowing a free flow of charges between the plate and the ground. The positive charge +Q will induce a negative charge on the side of the plate facing it.Electrons will flow into the plate from the ground to balance the Coulomb force, resulting in a net negative charge induced on the plate, and consequently, a net positive charge is left on the ground side of the plate.
02

Analyze what happens when the switch is opened

Once the switch is opened, the flow of charges between the plate and the ground is interrupted. The net negative charge induced on the plate when the positive charge +Q was near it gets trapped on the plate, as there is no path for it to flow to the ground.
03

Analyze the situation when +Q is removed

Finally, the charge +Q is removed from the vicinity of the plate. Since the switch is still open, the net negative charge that was induced on the plate cannot flow back to the ground and remains on the plate. Therefore, the plate stays charged with a net negative charge. Based on the analysis, the correct answer is: c) The plate is negatively charged.

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Most popular questions from this chapter

Two positive charges, each equal to \(Q\), are placed a distance \(2 d\) apart. A third charge, \(-0.2 Q\), is placed exactly halfway between the two positive charges and is displaced a distance \(x \ll d\) perpendicular to the line connecting the positive charges. What is the force on this charge? For \(x \ll d\), how can you approximate the motion of the negative charge?

A charge \(Q_{1}\) is positioned on the \(x\) -axis at \(x=a\). Where should a charge \(Q_{2}=-4 Q_{1}\) be placed to produce a net electrostatic force of zero on a third charge, \(Q_{3}=Q_{1}\), located at the origin? a) at the origin c) at \(x=-2 a\) b) at \(x=2 a\) d) at \(x=-a\)

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