In a metal wire, electrons are drifting to the right. What is the direction of conventional current?
ATo the right, following the electron motion
BTo the left, opposite to the electron motion
CThere is no conventional current when only electrons move
DPerpendicular to the wire axis
Conventional current is defined as the direction positive charges would flow to produce the same effect. Since electrons carry negative charge and drift to the right, conventional current points to the left. This historical convention (established before the electron was discovered) never leads to wrong answers as long as you apply it consistently — the physics is identical either way, since a rightward negative charge flow and a leftward positive charge flow produce the same electromagnetic effects.
Question 2 Multiple Choice
At a point in a conductor, ∇·J > 0. What is happening to the local charge density ρ at that point?
Aρ is increasing — current is converging and depositing charge
Bρ is decreasing — more current is leaving than arriving
Cρ is zero — the conductor is charge-neutral
Dρ is constant — the divergence of J doesn't affect charge density
The continuity equation ∂ρ/∂t + ∇·J = 0 directly links these quantities. If ∇·J > 0, more current is flowing out of the region than flowing in (net outflow). By charge conservation, this outflow must deplete the local charge, so ∂ρ/∂t = −∇·J < 0 — charge density is decreasing. Think of it as water: if more leaves a tank than enters, the level drops.
Question 3 True / False
In a metal wire carrying current, the drift velocity of electrons is in the same direction as the conventional current.
TTrue
FFalse
Answer: False
Electrons carry negative charge, so their drift is opposite to conventional current direction. Conventional current flows from high to low potential (positive terminal to negative terminal outside a battery), while electrons — driven by the electric field in the wire — move in the opposite direction, from low to high potential. The sign convention for current was established long before electrons were identified, and it defines current as the direction of positive charge flow.
Question 4 True / False
Electric current I = dQ/dt measures the rate at which charge flows through a cross-section of a conductor.
TTrue
FFalse
Answer: True
This is the definition of current: the instantaneous rate of charge transfer through a surface, measured in coulombs per second (amperes). It is a scalar — it tells you how much charge crosses the cross-section per unit time, but says nothing about where within the cross-section the charge is flowing. That spatial detail requires the current density vector J.
Question 5 Short Answer
Why is current density J a more fundamental description of current than the current I alone, and what information does I lose that J preserves?
Think about your answer, then reveal below.
Model answer: J is a vector field that describes the magnitude and direction of current flow at every point in space. I is a scalar that gives the total charge crossing a surface per second but discards all spatial detail about how that charge is distributed across the cross-section. When a conductor has a non-uniform cross-section, varying resistivity, or complicated geometry, J captures the local variation — including regions of higher or lower current density. I can always be recovered from J by integrating over a surface: I = ∬ J·dA.
A single wire can be described by I because the geometry is simple and current distributes uniformly. But in a complex conductor — like a semiconductor device, a plasma, or a wire that narrows — different regions carry different current densities. J = σE (Ohm's law in point form) connects the local field to the local current, which is the relationship that explains why narrow sections heat up more (higher J → higher power dissipation per volume). I alone can't give you that spatial picture.