What are SI units of n and q in the formula I = nqvdA?

Question

BlackTom AI · Accepted Answer

We start by restating the problem in our own words to ensure understanding: determine the SI units of n (number density) and q (charge) in the formula I = n q v d A.

Option a: n in particles, q in C/m3
This choice assigns n as a pure count of particles and q as charge per cubic meter. However, q typically represents a charge quantity (in coulombs) associated with each particle, not a density. The combination would not yield a consistent current dimension in I = n q v d A, since q should be the charge per particle, not a density.

Option b: n in particles/mole, q in C/particle
Here n is expressed in particles per mole, and q per particle. While n could be a count per unit amount in some contexts (like number of particles per mole), the standard current formula uses number density per volume, not per amount of substance. This mismatch with volume density makes it inaccurate for SI unit consistency in a current expression of this form.

Option c: n in moles, q in C
This suggests n has units of moles, which would contribute to a term like moles times charge, lacking the necessary dimensional alignment to yield current (A) when multiplied by velocity, area, etc. The dimensional analysis would fail because current requires charge per time, and just having moles as a count does not tie to a volumetric density or per-particle basis.

Option d: n in particles/m3, q in C
This option assigns n as a number density (particles per cubic meter) and q as a charge in coulombs per particle. When multiplied together, n q yields a charge per unit volume, and multiplying by velocity (m/s) and differential area (m^2) gives C/m^3 × m/s × m^2 = C·m/s / m^ etc., which aligns dimensionally with a current (A = C/s) when considering the full expression I = n q v d A with proper interpretation of v and dA. This is the consistent SI unit assignment for a current density flowing through a cross-sectional area, given per-particle charge and per-volume particle density.

In summary, the only option that preserves correct dimensional consistency for current in the formula I = n q v d A is option d, where n is expressed as particles per cubic meter and q as charge per particle (C). The other choices mix density concepts or per-particle versus per-volume in a way that would not yield the proper current units.

UCIC 202503 PHYS101 Quiz 10

What are SI units of n and q in the formula I = nqvdA?

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