The Physics
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# Electric Current

## Summary

• Electric current is the rate at which charge flows through a surface.
• Electric current is often just called current.
• As a scalar, current has magnitude only.
• The symbol for current is I (italic).
• In equation form, current can be written as…

non-calculus version calculus version
 Iave = Δq Δt
 I = lim Δq = dq Δt → 0 Δt dt
average current instantaneous current

Where…

 I = electric current [A] ∆q, dq = charge passing through some area [C] ∆t, dt = interval, instant of time [s]
• The SI unit of current is the ampère [A].
• The ampère is a fundamental unit defined by the results of an electromagnetic experiment.
• The unaccented spelling ampere is also acceptable in written English.
• The shortened form amp is often acceptable or even prefered.
• The SI unit of charge is the coulomb [C]
• The coulomb is a derived unit.
• One coulomb is the amount of charge transferred by one ampère of current in one second of time [C = A s].
• Current density is a quantity related to electric current.
• The symbol for current density is J (bold).
• As a vector, current density has magnitude and direction.
• By definition, current density is the product of charge density (ρ) and velocity (v).
• The magnitude of current density is also equivalent to the ratio of current (I) to area (A).
• In equation form, current density can be written as…

J = ρv  J = I A
vector definition magnitude equivalent

Where…  J, J = current density [A/m2] as a vector or its scalar magnitude I = electric current [A] ρ = charge density [C/m3] v = drift velocity [m/s] A = area [m2]
• The SI unit of current density is the ampère per square meter [A/m2].
• Microscopic Description of Current
• The macroscopic phenomena of electric current can be described by the net motion of microscopic charged particles.
• In equation form, the microscopic description of current and current density can be written…  I = nqAv J = nqv microscopic current microscopic current density
Where…  I = electric current [A] J = current density [A/m2] n = particle density [particles/m3] q = charge per particle [C] v, v = drift velocity [m/s] A = area [m2]