A glass rod is rubbed with silk and becomes positively charged. What happened to the total electric charge of the glass-and-silk system?
AIt increased — the rubbing created new positive charge on the glass
BIt stayed the same — electrons moved from the glass to the silk, leaving the glass positive and the silk equally negative
CIt decreased — some charge was lost as heat during the rubbing
DIt stayed the same only if the rubbing was done in an insulated environment
Charge is never created or destroyed — only transferred. When glass is rubbed with silk, electrons (negative charge carriers) migrate from the glass surface onto the silk. The glass loses electrons and becomes positively charged; the silk gains those electrons and becomes equally negatively charged. The total charge of the system (glass + silk) remains exactly zero, the same as before rubbing. Charge conservation applies everywhere, not just in insulated environments.
Question 2 Multiple Choice
A neutron (charge = 0) undergoes beta decay and produces a proton (charge = +1) and an electron (charge = −1). What does charge conservation require about the antineutrino emitted in this process?
AThe antineutrino must carry charge +1 to balance the proton
BThe antineutrino must carry charge −1 to cancel the electron
CThe antineutrino must carry zero charge, since the proton and electron already balance each other
DCharge conservation doesn't constrain the antineutrino's charge in nuclear processes
Before decay: total charge = 0 (neutron). After decay: proton (+1) + electron (−1) + antineutrino = 0 requires the antineutrino to carry zero charge. And indeed, neutrinos and antineutrinos are electrically neutral. Charge conservation applies in every physical process without exception — nuclear, atomic, particle — and is precise enough to constrain properties of particles. Option D is false: charge conservation holds universally.
Question 3 True / False
When an electron and a positron (anti-electron) are created together from a high-energy gamma ray, net electric charge is created in that region of space.
TTrue
FFalse
Answer: False
In electron-positron pair production, a gamma ray creates one electron (charge −1) and one positron (charge +1) simultaneously. The total charge created is −1 + 1 = 0. No net charge is created. This is not coincidence — charge conservation requires that any particle created from a chargeless photon must be accompanied by its antiparticle with equal and opposite charge. The total charge of the universe remains constant in every process.
Question 4 True / False
The continuity equation ∂ρ/∂t + ∇·J⃗ = 0 states that charge can disappear from one location and reappear instantaneously at a distant location.
TTrue
FFalse
Answer: False
The continuity equation expresses the opposite: charge is locally conserved. If charge density decreases in a region (∂ρ/∂t < 0), it can only decrease because charge is flowing out through the boundary (∇·J⃗ > 0). Charge cannot teleport — it must flow continuously through space. This is the 'local' form of conservation: not only is the total charge in the universe constant, but charge cannot jump from one place to another without traversing the space in between. This local conservation is a stronger statement than global conservation.
Question 5 Short Answer
Explain what the continuity equation ∂ρ/∂t + ∇·J⃗ = 0 means physically, and why it is called a 'local' conservation law.
Think about your answer, then reveal below.
Model answer: The continuity equation says that the rate of change of charge density at any point in space equals the negative of the divergence of current density. In plain terms: if charge is leaving a small region (∇·J⃗ > 0, net outflow), then the charge density inside that region must be decreasing (∂ρ/∂t < 0) at exactly the same rate — nothing more, nothing less. It is 'local' because it holds at every point in space independently: charge cannot disappear here and appear elsewhere without flowing continuously through the intervening space. This rules out teleportation of charge. By contrast, a 'global' conservation law would only say that the total charge in the universe is constant, without specifying that it flows.
The distinction between local and global conservation is physically important. A global law could be satisfied by charge vanishing in one galaxy and appearing in another simultaneously. The continuity equation rules this out — it enforces charge accounting at every infinitesimal volume. This local form is what is actually encoded in Maxwell's equations and what underpins Kirchhoff's current law: current can't pile up at a circuit node, it must flow through.