Current

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Table of Contents

• Current
  • Key Definitions
  • Current
    • $I=\frac{dQ}{dt}\approx \frac{\mathrm{\Delta }Q}{\mathrm{\Delta }t}[A]$
      • $1A=1\frac{C}{s}$
  • Direction of Current
    • $I=\frac{d(+q)}{dt}$
    • Drift Velocity
      • $I=\frac{dQ}{dt}=n|q|v_{d}A$
  • Mechanics of Current
  • Current Density
    • $J=\frac{dI}{dA}$
    • $\overrightarrow{J}=n|q|{\overrightarrow{v}}_d$

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Current

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Key Definitions

Electric Current - flow of through a medium

Volume charge density - current per unit area

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Current

Defined as

$I=\frac{dQ}{dt}\approx \frac{\mathrm{\Delta }Q}{\mathrm{\Delta }t}[A]$

The unit of current is the Ampere:

$1A=1\frac{C}{s}$

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Direction of Current

Current is defined by the flow of positive charge:

$I=\frac{d(+q)}{dt}$

However, in a conducting wire, the negatively charged electrons are moving.

Thus, current flowing through a wire actually means the negative flow of electrons through a wire:

Drift Velocity

Free moving electrons collide with other electrons and atoms. The average velocity of free charges is called the drift velocity, $v_d$, and it is the direction opposite to the electric field for the electrons.

Collisions transfer energy to the conductor, thus requiring a constant supply of energy to maintain a steady current:

$I=\frac{dQ}{dt}=n|q|v_{d}A$

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Mechanics of Current

On the subatomic level, electrons bounce around within a conducting wire at the order of ${10}^{6}m/s$, but the thermal motion of electrons is random and creates no net current.

To produce non-trivial current through a wire, we need to apply an which will exert a net force on the charges by

The average velocity of the charges is the drift velocity and is about ${10}^{-4}m/s$

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Current Density

Volume charge density - current per unit area:

$J=\frac{dI}{dA}$

Alternatively, given drift velocity:

$\overrightarrow{J}=n|q|{\overrightarrow{v}}_d$