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Two identical metal spheres carry charges +6 μC and −2 μC. They are brought into contact and then separated. Determine the final charge on each sphere.
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Total charge before contact $${Q}_{\text{total}}=+6 \mu \text{C}+(-2 \mu \text{C})=+4 \mu \text{C}$$ Identical conductors share charge equally $${Q}_{\text{each}}=\frac{+4 \mu \text{C}}{2}=+2 \mu \text{C}$$ Each sphere carries +2 μC after separation.
A glass rod is rubbed with silk. The rod acquires a charge of +8 nC. Indicate whether the silk’s charge is greater than, less than, or equal to 8 nC in magnitude? Justify your response.
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Equal to 8 nC in magnitude. Conservation of charge requires that every electron removed from the glass transfers to the silk. The silk gains −8 nC, so its magnitude equals 8 nC.
A positively charged rod is held near a neutral metal sphere without touching it. Describe the charge distribution on the sphere and explain why a net force acts on the sphere?
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The positive rod attracts free electrons in the metal sphere toward the near side. The near side becomes negatively charged; the far side becomes positively charged. The net charge on the sphere remains zero. However, the negative charges on the near side are closer to the rod than the positive charges on the far side. Because electrostatic force is stronger at shorter distances, the attractive force on the near side exceeds the repulsive force on the far side. The sphere experiences a net attractive force toward the rod.
Indicate whether an insulator can be polarized by a nearby charged object? Justify your response using qualitative reasoning beyond referencing equations.
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Yes, an insulator can be polarized. Although electrons in an insulator cannot move freely between atoms, the electron cloud around each molecule shifts slightly. The side of each molecule nearest the external charge develops a small induced charge of opposite sign. Across many molecules, this produces a net surface charge and a weak attraction.
A metal sphere has a net charge of −5 μC. After a process, its charge becomes −2 μC. Describe what happened in terms of electron transfer?
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The sphere lost 3 μC of negative charge. Because charging involves electron transfer, electrons moved from the sphere to its surroundings. The number of electrons transferred $$n=\frac{\Delta q}{e}=\frac{3\times {10}^{-6}}{1.60\times {10}^{-19}}$$ $$n\approx 1.88\times {10}^{13}\text{ electrons}$$ Approximately 1.88 × 10¹³ electrons left the sphere.
A system consists of two objects with charges +4 μC and −1 μC. No charge enters or leaves the system. Indicate whether the total charge of the system can change? Justify your response.
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The total charge cannot change. Conservation of charge requires that net charge remains constant when no charge crosses the system boundary. The total remains +3 μC regardless of any internal redistribution.
A negatively charged metal sphere is connected to Earth by a wire. Describe the direction of electron flow and the final charge on the sphere.
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Electrons flow from the sphere through the wire into Earth. Earth is so large that the added electrons produce no measurable change in Earth’s charge. The sphere’s excess negative charge is neutralized. The sphere’s final charge is zero.
A student charges a metal sphere by induction using a positive rod and a ground connection. The student accidentally removes the rod before disconnecting the ground wire. Describe how the final charge on the sphere would differ from the intended result? Briefly justify your answer.
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The sphere ends up neutral instead of negatively charged. While the rod was nearby, electrons flowed from Earth into the sphere. When the rod is removed first, the external field disappears and nothing holds the extra electrons on the sphere. Those electrons flow back to Earth through the still-connected ground wire. The sphere returns to its original neutral state.
Is the process described in Question 8 consistent with conservation of charge? Justify your response.
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Yes. At every stage, the total charge of the rod-sphere-Earth system remains constant. Electrons flow between the sphere and Earth, but no charge is created or destroyed. The final state — neutral sphere, unchanged rod, unchanged Earth — has the same total charge as the initial state.