Conservation of Electric Charge and Charging

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AP Physics 2 › Conservation of Electric Charge and Charging

Questions 1 - 10
1

A neutral metal sphere on an insulating stand is touched by a rod with charge $-Q$ and then separated. Which statement best describes the sphere’s final charge?​

The sphere becomes positively charged because electrons are created on its surface.

The sphere becomes negatively charged because induction transfers electrons without contact.

The sphere becomes negatively charged because electrons transfer by contact.

The sphere remains neutral because neutral objects contain no charges.

Explanation

This question tests conservation of electric charge and charging. When a charged rod touches a neutral conductor, electrons transfer between them until they reach the same electric potential, a process called charging by conduction. Since the rod has charge -Q (excess electrons) and touches the neutral sphere, electrons flow from the rod to the sphere, giving the sphere a negative charge. The total charge of the system (rod + sphere) remains constant at -Q, though it redistributes between the two objects. Choice C incorrectly assumes neutral objects contain no charges, when actually they have equal amounts of positive and negative charge. When solving charging problems, remember that charge transfers by contact involve actual movement of electrons, and the total charge is always conserved.

2

Two identical metal spheres start neutral and are touching. A negatively charged rod is brought near sphere 1 (no contact), then the spheres are separated, then the rod is removed. Which statement best describes the final charges?

Sphere 1 is positive and sphere 2 is negative because electrons moved toward the rod.

Both spheres are negative because electrons transferred from the rod by induction.

Sphere 1 is negative and sphere 2 is positive because charge separated while touching.

Both spheres are neutral because the rod never touched either sphere.

Explanation

This question tests conservation of electric charge and charging. When the negative rod approaches sphere 1, it repels electrons through the contact point into sphere 2, making sphere 1 positive (electron deficit) and sphere 2 negative (electron excess). Separating the spheres while the rod is still nearby locks in this charge separation - sphere 1 remains positive and sphere 2 remains negative even after the rod is removed. The total charge of both spheres together remains zero, conserving charge. Choice B incorrectly suggests the rod can transfer electrons without contact, but the charge separation occurs through electron movement between the touching spheres. To solve multi-object induction problems, track electron flow between connected conductors before they separate.

3

A charged rod is brought near a neutral conductor, causing polarization. The rod is then removed without any contact or grounding. Which statement best describes the conductor’s final net charge?

It is charged with the same sign as the rod because polarization creates net charge.

It is oppositely charged because induction always transfers electrons to the conductor.

It has no charges anywhere because the rod removed the conductor’s electrons.

It is neutral because charges redistributed temporarily but no net charge was transferred.

Explanation

This question tests conservation of electric charge and charging. When a charged rod approaches a conductor, it causes polarization - electrons redistribute within the conductor but none enter or leave, so the net charge remains zero. When the rod is removed, the polarized charges redistribute back to uniform distribution, and the conductor returns to its original neutral state with zero net charge. No charge transfers between rod and conductor without contact or grounding. Choice B incorrectly claims polarization creates net charge, but it only rearranges existing charges. Remember that polarization is temporary charge separation that requires no charge transfer - removing the external influence returns the conductor to neutral.

4

A neutral metal sphere is touched to a negatively charged sphere and then separated. Which conclusion follows from conservation of electric charge?

The total charge of the two-sphere system is unchanged, though it may redistribute.

The total charge becomes zero because opposite charges cancel and vanish on contact.

The neutral sphere stays neutral because neutral objects contain no mobile charges.

The negatively charged sphere becomes more negative because contact creates extra electrons.

Explanation

This question tests conservation of electric charge and charging. When conductors with different charges touch, electrons flow between them until they reach the same electric potential, redistributing the total charge. The initial total charge is 0 + (-Q) = -Q, and by conservation of charge, the final total must also be -Q, now shared between both spheres. Neither sphere remains at its initial charge - the neutral sphere becomes negative and the charged sphere becomes less negative. Choice B incorrectly suggests opposite charges cancel and vanish, but charge cannot be destroyed, only redistributed. When analyzing charge sharing, always apply conservation: the sum of all charges before contact equals the sum after contact.

5

A negatively charged rod is held near a neutral metal sphere without touching. The sphere is grounded, then the ground is removed, then the rod is removed. Which statement best describes the sphere’s final charge?

The sphere is negatively charged because electrons moved from the rod onto the sphere through air.

The sphere is neutral because grounding removes all charges from the sphere.

The sphere is positively charged because electrons left through the ground during induction.

The sphere is positively charged because positive charge flowed from the rod into the sphere.

Explanation

This question tests conservation of electric charge and charging. In charging by induction, a charged object influences charge distribution in a conductor without touching it - the negative rod repels electrons in the sphere to the far side, leaving the near side positive. When the sphere is grounded while the rod is nearby, electrons flow from the sphere through the ground wire to escape the repulsion, leaving the sphere with a net positive charge. After removing the ground and then the rod, this positive charge redistributes uniformly on the sphere. Choice C incorrectly suggests electrons can jump through air from rod to sphere, but charge transfer requires contact or a conducting path. To analyze induction problems, track electron movement step-by-step and remember that grounding provides a path for charge to flow.

6

A negatively charged rod is brought near (without touching) a neutral metal sphere on an insulating stand. No grounding occurs. Which statement best describes the sphere’s final net charge after the rod is removed?

It is positive because electrons are pushed off the sphere and lost to the surroundings.

It is zero because charges only separate temporarily and then recombine, conserving net charge.

It is negative because electrons are pulled onto the sphere from the rod through the air gap.

It is zero because a neutral object contains no charges that can be rearranged.

Explanation

This question tests conservation of electric charge and charging. When a charged rod is brought near a neutral conductor without touching or grounding, it only causes temporary charge separation (polarization) within the conductor—electrons move to one side, leaving positive charge on the other. However, the total number of electrons and protons in the sphere remains unchanged, so the net charge stays zero. When the rod is removed, the separated charges recombine, returning the sphere to its original neutral state with zero net charge. Choice A incorrectly suggests electrons can jump through air—at typical voltages, air is an insulator preventing charge transfer without contact. For polarization without grounding: charge separates temporarily but net charge always remains unchanged.

7

A glass rod becomes positively charged after rubbing with silk. Which statement best describes what happened to the charges during rubbing?

Protons were transferred from the silk to the glass, making the glass positively charged.

The glass became positive because neutral objects contain no electrons to begin with.

Positive charge was created in the glass due to friction, increasing total charge.

Electrons were transferred from the glass to the silk, leaving the glass with net positive charge.

Explanation

This question tests conservation of electric charge and charging. When glass is rubbed with silk, friction provides energy to overcome the binding forces holding electrons to atoms, allowing electron transfer between the materials. Glass has a weaker hold on its outer electrons compared to silk, so electrons transfer from glass to silk during rubbing, leaving the glass with a deficit of electrons (positive charge) and the silk with excess electrons (negative charge). The total charge of the glass-silk system remains zero, conserving charge. Choice B incorrectly suggests protons move—protons are bound in atomic nuclei and cannot transfer during rubbing; only electrons are mobile. In triboelectric charging, remember: only electrons transfer, and the material losing electrons becomes positive.

8

A glass rod is charged positively and touches a neutral electroscope knob, then is removed. Which statement best describes the electroscope’s final state?

The electroscope becomes negatively charged because protons transfer from the rod to it.

The electroscope becomes neutral because positive charge is destroyed when the rod leaves.

The electroscope becomes positively charged because electrons transfer from it to the rod.

The electroscope remains neutral because contact cannot transfer charge.

Explanation

This question tests conservation of electric charge and charging. When a positively charged glass rod touches a conductor, charge transfer occurs through electron movement - the rod's positive charge means it has a deficit of electrons. Electrons from the neutral electroscope are attracted to and transfer onto the positive rod, leaving the electroscope with fewer electrons and thus a net positive charge. After the rod is removed, the electroscope retains this positive charge. Choice B incorrectly suggests protons transfer, but protons are bound in atomic nuclei and don't move during electrostatic charging - only electrons transfer. When analyzing contact charging, remember that positive charge means electron deficit, and electrons always move from where they're more concentrated to where they're less concentrated.

9

A neutral conducting sphere is touched by a negatively charged sphere and then they are separated. Which statement best describes the total charge of the two-sphere system?

The total charge decreases because some charge is destroyed as heat.

The total charge becomes zero because opposite charges cancel when separated.

The total charge stays the same because charge is conserved during conduction.

The total charge increases because contact creates extra electrons.

Explanation

This question tests conservation of electric charge and charging. Charge conservation is a fundamental principle stating that the total charge in an isolated system remains constant - charge cannot be created or destroyed. When the negatively charged sphere touches the neutral sphere, electrons redistribute between them, but the total number of electrons (and thus total charge) in the two-sphere system remains exactly the same as initially. The charge simply redistributes from one sphere to both spheres. Choice D incorrectly suggests charge can be destroyed as heat, confusing charge with energy - while energy can convert to heat, charge itself is always conserved. To solve any charging problem, apply charge conservation: count total charge before and after any process.

10

Two identical metal spheres on insulating stands have net charges $+4,\mu\text{C}$ and $-2,\mu\text{C}$. They touch and are separated. Which statement best describes the final charge on each sphere?

Each sphere ends with $0,\mu\text{C}$ because charges cancel and vanish during touching.

Each sphere ends with $+2,\mu\text{C}$ because the negative charge is destroyed on contact.

Each sphere ends with $+1,\mu\text{C}$ because charge redistributes equally while total charge is conserved.

One sphere ends with $+4,\mu\text{C}$ and the other with $-2,\mu\text{C}$ because charge cannot move in conductors.

Explanation

This question tests conservation of electric charge and charging. When two identical conducting spheres touch, charge redistributes between them until they reach the same electric potential, which for identical spheres means equal charge. The total initial charge is (+4 μC) + (-2 μC) = +2 μC, and this total must be conserved throughout the process. Since the spheres are identical, this +2 μC divides equally, giving each sphere +1 μC after separation. Choice C incorrectly assumes opposite charges "cancel and vanish"—charge is conserved, not destroyed; the charges redistribute but the total remains +2 μC. When identical conductors touch, always calculate total charge first, then divide equally between them.

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