Conservation of Electric Charge and Charging - AP Physics 2

  1. A positively charged glass rod is brought near (but not touching) a neutral metal can on an insulating stand. Which statement best describes the can while the rod is nearby?
    Answer: The can remains net neutral but becomes polarized with excess electrons on the near side. This question tests conservation of electric charge and charging. When a positively charged rod approaches a neutral conductor, it attracts the conductor's mobile electrons toward the near side and repels positive charges (actually absence of electrons) to the far side - this redistribution is called polarization. The can remains electrically neutral overall because no charge enters or leaves it; the same number of protons and electrons are present, just rearranged. The near side becomes negative (excess electrons) and the far side becomes positive (deficit of electrons). Choice A incorrectly suggests positive charges can jump across air, but only electrons are mobile in metals. Remember that polarization rearranges existing charges without changing the net charge - total charge is conserved.
  2. A neutral electroscope is charged by induction using a negatively charged rod: the rod is brought near, the electroscope is grounded, then the ground is removed first, and finally the rod is removed. Which statement best describes the electroscope's final net charge?
    Answer: It becomes positively charged because electrons leave to ground while the rod is nearby. This question tests conservation of electric charge and charging. When a negatively charged rod approaches a neutral electroscope, it repels electrons downward into the leaves and attracts positive regions upward, polarizing the electroscope. Grounding while the rod is present allows electrons to escape from the electroscope to Earth, leaving a deficit of electrons (positive charge). Removing ground first, then the rod, traps this positive charge on the electroscope permanently. Choice A incorrectly claims the rod transfers electrons without contact—induction involves charge separation within the conductor, not transfer between objects; only grounding allows actual charge transfer. For charging by induction: the final charge is always opposite to the inducing charge when proper grounding occurs.
  3. A charged metal sphere is brought into contact with a neutral metal sphere; both are on insulating stands. After contact, they are separated. Which statement best describes the total charge of the two-sphere system?
    Answer: It is unchanged because charge is conserved; contact only redistributes charge between spheres. This question tests conservation of electric charge and charging. When a charged sphere contacts a neutral sphere, charge redistributes between them through electron transfer, but the total charge of the two-sphere system must remain constant due to charge conservation. If the first sphere initially has charge Q and the second has 0, the total system charge is Q before contact and remains Q after separation, though now distributed between both spheres. The charge redistributes to equalize electric potential, but no charge is created, destroyed, or lost from the isolated system. Choice C incorrectly suggests charge is "used up"—charge is a conserved quantity that cannot be consumed or destroyed in any process. Remember: in any isolated system, total charge before equals total charge after, regardless of how charge redistributes.
  4. A positively charged rod touches a neutral metal electroscope and is removed. Which statement best describes the electroscope afterward?
    Answer: It becomes positively charged because electrons leave it during contact charging This question tests conservation of electric charge and charging. When a positively charged rod touches a neutral conductor, electrons from the conductor are attracted to and neutralize some positive charge on the rod, leaving the conductor with a deficit of electrons (positive charge). This is charging by conduction—direct contact allows electron transfer. The electroscope becomes positively charged because it lost electrons to the rod, not because positive charges moved (protons are fixed in atomic nuclei). Choice B incorrectly assumes positive charges can move between objects, when only electrons are mobile in conductors. Key principle: in metals, only electrons move; positive charge results from electron deficit.
  5. A negatively charged rod is held near a neutral conductor while it is grounded; the ground is removed first, then the rod. Which statement best describes the conductor's final charge?
    Answer: Positive, because electrons leave the conductor to the ground while the rod is nearby This question tests conservation of electric charge and charging. During induction charging with grounding, the negatively charged rod repels electrons in the conductor, causing them to flow to ground, leaving the conductor positively charged. The critical step is removing the ground connection while the rod is still present—this traps the positive charge on the conductor. When the rod is finally removed, the conductor retains its positive charge. Choice D incorrectly suggests protons can move, but in solid conductors only electrons are mobile—positive charge results from electron deficit, not proton gain. Key sequence: the ground must be disconnected before removing the inducing charge.
  6. A glass rod is charged positively and touches a neutral electroscope knob, then is removed. Which statement best describes the electroscope's final state?
    Answer: The electroscope becomes positively charged because electrons transfer from it to the rod. 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.
  7. A neutral metal sphere is brought near a negatively charged rod without touching. The sphere is then grounded briefly and the ground is removed first. Which statement best describes the sphere's final net charge?
    Answer: It becomes positively charged because electrons leave to Earth while the rod is nearby. This question tests conservation of electric charge and charging. When a negatively charged rod is brought near a neutral conductor, it repels electrons within the conductor to the far side, creating charge separation (polarization). When the sphere is grounded while the rod is nearby, electrons flow from the sphere to Earth (ground), leaving the sphere with a deficit of electrons and thus positively charged. Removing the ground first, then the rod, traps this positive charge on the sphere. Choice C incorrectly claims induction cannot change net charge—while induction alone cannot, grounding during induction allows charge to flow in or out, changing the net charge. To solve induction problems: identify charge movement during grounding, then determine what charge remains when connections are removed.
  8. 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?
    Answer: It is neutral because charges redistributed temporarily but no net charge was transferred. 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.
  9. A positively charged rod is brought near a neutral metal sphere on an insulating stand without touching. Which statement best describes the sphere?
    Answer: The sphere remains net neutral but becomes polarized, with negative charge nearer the rod This question tests conservation of electric charge and charging. When a charged object is brought near a conductor without touching, it causes charge separation (polarization) through induction, but no charge transfer occurs. The positive rod attracts electrons within the neutral sphere toward the near side, leaving positive charge on the far side. The sphere remains electrically neutral overall because no electrons enter or leave it—they only redistribute internally. Choice A incorrectly assumes electrons can jump across air gaps during induction, violating the principle that charge transfer requires contact or a conducting path. Remember: induction causes charge separation within a conductor but preserves net neutrality without grounding.
  10. A positively charged rod is brought near a neutral metal sphere, but neither is grounded and they never touch. Which statement best describes the final net charges?
    Answer: Both objects keep their original net charges, though the sphere's charges redistribute. This question tests conservation of electric charge and charging. When a charged object is brought near a conductor without touching or grounding, it causes charge redistribution (polarization) within the conductor but cannot change the conductor's net charge. The positive rod attracts electrons to the near side of the sphere and repels them from the far side, but the total number of electrons in the sphere remains unchanged - it stays neutral. The rod also maintains its original positive charge since no charge transfers occur. Choice B incorrectly suggests the sphere becomes positively charged, confusing induced charge separation with actual charging. Remember that without contact or grounding, induction only rearranges existing charges, never changes the net charge.
  11. A +8 μC+8\,\mu\text{C} metal sphere touches an identical −2 μC-2\,\mu\text{C} metal sphere, then they separate. Which statement best describes final charges?
    Answer: Both spheres are +3 μC+3\,\mu\text{C} because total charge is conserved and shared equally This question tests conservation of electric charge and charging. When identical metal spheres with different charges touch, electrons flow from the more negative (or less positive) sphere to the more positive one until both reach the same potential. The total initial charge is +8 μC + (-2 μC) = +6 μC, which must be conserved. For identical spheres, this total charge distributes equally: +6 μC ÷ 2 = +3 μC each. Choice D incorrectly assumes opposite charges must cancel to zero on each sphere, misunderstanding that charges redistribute between spheres, not within individual spheres. Remember: charge flows between conductors to equalize potential, conserving total charge.
  12. A negatively charged rod is brought near (without touching) a neutral conducting sphere on an insulating stand. Which statement best describes the sphere's charge?
    Answer: The sphere remains net neutral but becomes polarized with charges separated. This question tests conservation of electric charge and charging. When a charged object is brought near a conductor without touching, it induces charge separation through electrostatic forces - this process is called induction. The negatively charged rod repels electrons in the sphere to the far side, leaving the near side with a deficit of electrons (positive). However, since no charge transfers between the rod and sphere, the sphere's total charge remains zero - it's neutral but polarized. Choice A incorrectly suggests electrons jump across the air gap, which doesn't happen without an extremely high voltage or physical contact. To solve induction problems, remember that charges redistribute within conductors but the net charge only changes if there's actual charge transfer.
  13. A neutral metal sphere on an insulating stand is touched by a rod with charge −Q-Q and then separated. Which statement best describes the sphere's final charge?​
    Answer: The sphere becomes negatively charged because electrons transfer by contact. 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.
  14. Two identical insulating spheres have charges +3 μC+3\,\mu\text{C} and −1 μC-1\,\mu\text{C}. They are briefly touched together and separated. Which statement best describes the final charges?
    Answer: They remain +3 μC+3\,\mu\text{C} and −1 μC-1\,\mu\text{C} because charge does not flow freely through insulators. This question tests conservation of electric charge and charging. Unlike conductors where charge flows freely, insulators hold charge localized where it was placed because electrons cannot move freely through the material. When two charged insulating spheres touch, minimal charge transfer occurs because the charges are trapped in their original locations by the insulating material's atomic structure. The spheres essentially retain their original charges of +3 μC and -1 μC after separation. Choice B incorrectly assumes charge redistributes equally—this only happens with conductors where charge can flow freely; insulators prevent such redistribution. When dealing with insulators, remember: charge remains localized and does not redistribute significantly even during contact.
  15. 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?
    Answer: The total charge stays the same because charge is conserved during conduction. 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.
  16. A neutral metal sphere touches a −6 μC-6\,\mu\text{C} metal sphere, then they separate. Which statement best describes the final charges?
    Answer: Both spheres are −3 μC-3\,\mu\text{C} because total charge is conserved and shared equally 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 initial total charge is -6 μC + 0 μC = -6 μC, and this total must be conserved. Since the spheres are identical, they share this charge equally: -6 μC ÷ 2 = -3 μC each. Choice B incorrectly assumes neutral objects cannot gain or lose charge, failing to recognize that neutral simply means equal positive and negative charges that can separate. The key strategy is: when identical conductors touch, total charge is conserved and shared equally between them.
  17. A −4 μC-4\,\mu\text{C} metal sphere touches an identical neutral sphere and is then separated. Which statement best describes the final charges?
    Answer: Both spheres are −2 μC-2\,\mu\text{C} because total charge is conserved and shared equally This question tests conservation of electric charge and charging. When identical conducting spheres touch, charge flows between them until they reach equal electric potential, which means equal charge for identical spheres. The total initial charge is -4 μC + 0 μC = -4 μC, and charge conservation requires this total to remain constant. The charge distributes equally between the identical spheres: -4 μC ÷ 2 = -2 μC each. Choice A incorrectly suggests electrons can replicate or be created, violating charge conservation—charge can only be separated or redistributed, never created or destroyed. The principle to remember: total charge before contact equals total charge after separation.
  18. A negatively charged balloon is rubbed on hair and then stuck to a neutral wall without touching metal. Which conclusion about charging best follows?
    Answer: The wall becomes polarized, producing attraction without net charge transfer to the wall. This question tests conservation of electric charge and charging. The negatively charged balloon induces polarization in the wall's molecules - even though the wall is an insulator, charges within molecules can shift slightly. The balloon's negative charge repels electrons in wall molecules slightly away, leaving the near surface with a slight positive charge that attracts the balloon. Crucially, no net charge transfers to the wall; it remains neutral overall but develops an induced dipole moment. Choice B incorrectly suggests electrons flow through air into the wall, which would require either contact or extremely high voltage to ionize the air. When analyzing electrostatic attraction to insulators, remember that polarization can create forces without any net charge transfer.
  19. A neutral metal sphere is touched by a rod with charge −6.0 μC-6.0\,\mu\text{C}, then the rod is removed. Which statement best describes the sphere's final charge?
    Answer: The sphere becomes negatively charged because electrons transfer by contact. This question tests conservation of electric charge and charging. When a charged rod touches a neutral conductor, electrons transfer between them to equalize the electric potential, resulting in both objects sharing the original charge. Since the rod is negatively charged (-6.0 μC), it has excess electrons that will flow onto the neutral sphere during contact. The sphere gains electrons and becomes negatively charged, while the rod loses some negative charge but remains negative. Choice B incorrectly suggests electrons are destroyed, violating charge conservation - charges cannot be created or destroyed, only transferred. When analyzing charging problems, remember that only electrons move in solid conductors, and total charge is always conserved.
  20. A neutral metal can is charged by induction using a positively charged rod and a ground wire. After removing ground then rod, which statement best describes the can?
    Answer: The can becomes negatively charged because electrons enter from ground during induction. This question tests conservation of electric charge and charging. In charging by induction with grounding, the positive rod attracts electrons in the can toward the near side, pushing electrons on the far side to flow into the ground. When ground is removed (while the rod is still present), the can is left with extra electrons, making it negatively charged. Removing the rod last allows these extra electrons to redistribute throughout the can. Choice D incorrectly claims positive charges flow from ground - in reality, only electrons move in conductors, and the can gains electrons from Earth. To master induction charging, visualize electron movement and remember the critical sequence: bring charged object near, connect ground, disconnect ground, then remove charged object.

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