In physics, a drift velocity is the average velocity attained by charged particles, such as electrons, in a material due to an electric field. In general, an electron in a conductor will propagate randomly at the Fermi velocity, resulting in an average velocity of zero. Applying an electric field adds to this random motion a small net flow in one direction; this is the drift.
Drift velocity of electrons
Drift velocity is proportional to current. In a resistive material, it is also proportional to the magnitude of an external electric field. Thus Ohm's law can be explained in terms of drift velocity. The law's most elementary expression is:
where u is drift velocity, μ is the material's electron mobility, and E is the electric field. In the MKS system, these quantities' units are m/s, m2/(V·s), and V/m, respectively.
When a potential difference is applied across a conductor, free electrons gain velocity in the direction, opposite to the electric field between successive collisions (and lose velocity when traveling in the direction of the field), thus acquiring a velocity component in that direction in addition to its random thermal velocity. As a result, there is a definite small drift velocity of electrons, which is superimposed on the random motion of free electrons. Due to this drift velocity, there is a net flow of electrons opposite to the direction of the field.
The formula for evaluating the drift velocity of charge carriers in a material of constant cross-sectional area is given by:[1]
where u is the drift velocity of electrons, j is the current density flowing through the material, n is the charge-carrier number density, and q is the charge on the charge-carrier.
This can also be written as:
But the current density and drift velocity, j and u, are in fact vectors, so this relationship is often written as:
Electricity is most commonly conducted through copper wires. Copper has a density of 8.94 g/cm3 and an atomic weight of 63.546 g/mol, so there are 140685.5 mol/m3. In one mole of any element, there are 6.022×1023 atoms (the Avogadro number). Therefore, in 1 m3 of copper, there are about 8.5×1028 atoms (6.022×1023 × 140685.5 mol/m3). Copper has one free electron per atom, so n is equal to 8.5×1028 electrons per cubic metre.
Assume a current I = 1 ampere, and a wire of 2 mm diameter (radius = 0.001 m). This wire has a cross sectional area A of π × (0.001 m)2 = 3.14×10−6 m2 = 3.14 mm2. The charge of one electron is q = −1.6×10−19 C. The drift velocity therefore can be calculated:
Therefore, in this wire, the electrons are flowing at the rate of 23 μm/s. At 60Hz alternating current, this means that, within half a cycle, on average the electrons drift less than 0.2 μm. In context, at one ampere around 3×1016 electrons will flow across the contact point twice per cycle. But out of around 1×1022 movable electrons per meter of wire, this is an insignificant fraction.
By comparison, the Fermi flow velocity of these electrons (which, at room temperature, can be thought of as their approximate velocity in the absence of electric current) is around 1570 km/s.[2]
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In physics a drift velocity is the average velocity attained by charged particles such as electrons in a material due to an electric field In general an electron in a conductor will propagate randomly at the Fermi velocity resulting in an average velocity of zero Applying an electric field adds to this random motion a small net flow in one direction this is the drift Drift velocity of electrons Drift velocity is proportional to current In a resistive material it is also proportional to the magnitude of an external electric field Thus Ohm s law can be explained in terms of drift velocity The law s most elementary expression is u m E displaystyle u mu E where u is drift velocity m is the material s electron mobility and E is the electric field In the MKS system these quantities units are m s m2 V s and V m respectively When a potential difference is applied across a conductor free electrons gain velocity in the direction opposite to the electric field between successive collisions and lose velocity when traveling in the direction of the field thus acquiring a velocity component in that direction in addition to its random thermal velocity As a result there is a definite small drift velocity of electrons which is superimposed on the random motion of free electrons Due to this drift velocity there is a net flow of electrons opposite to the direction of the field Contents 1 Experimental measure 2 Numerical example 3 See also 4 References 5 External linksExperimental measure EditThe formula for evaluating the drift velocity of charge carriers in a material of constant cross sectional area is given by 1 u j n q displaystyle u j over nq where u is the drift velocity of electrons j is the current density flowing through the material n is the charge carrier number density and q is the charge on the charge carrier This can also be written as j n q u displaystyle j nqu But the current density and drift velocity j and u are in fact vectors so this relationship is often written as J r u displaystyle mathbf J rho mathbf u where r n q displaystyle rho nq is the charge density SI unit coulombs per cubic metre In terms of the basic properties of the right cylindrical current carrying metallic ohmic conductor where the charge carriers are electrons this expression can be rewritten as citation needed u m s D V r e f ℓ displaystyle u m sigma Delta V over rho ef ell where u is again the drift velocity of the electrons in m s 1 m is the molecular mass of the metal in kg s is the electric conductivity of the medium at the temperature considered in S m DV is the voltage applied across the conductor in V r is the density mass per unit volume of the conductor in kg m 3 e is the elementary charge in C f is the number of free electrons per atom ℓ is the length of the conductor in mNumerical example EditElectricity is most commonly conducted through copper wires Copper has a density of 8 94 g cm3 and an atomic weight of 63 546 g mol so there are 140685 5 mol m3 In one mole of any element there are 6 022 1023 atoms the Avogadro number Therefore in 1 m3 of copper there are about 8 5 1028 atoms 6 022 1023 140685 5 mol m3 Copper has one free electron per atom so n is equal to 8 5 1028 electrons per cubic metre Assume a current I 1 ampere and a wire of 2 mm diameter radius 0 001 m This wire has a cross sectional area A of p 0 001 m 2 3 14 10 6 m2 3 14 mm2 The charge of one electron is q 1 6 10 19 C The drift velocity therefore can be calculated u I n A q 1 C s 8 5 10 28 m 3 3 14 10 6 m 2 1 6 10 19 C 2 3 10 5 m s displaystyle begin aligned u amp I over nAq amp frac 1 text C text s left 8 5 times 10 28 text m 3 right left 3 14 times 10 6 text m 2 right left 1 6 times 10 19 text C right amp 2 3 times 10 5 text m text s end aligned Dimensional analysis u A electron m 3 m 2 C electron C s 1 m C m s displaystyle u dfrac text A dfrac text electron text m 3 cdot text m 2 cdot dfrac text C text electron dfrac dfrac text C text s dfrac 1 text m cdot text C dfrac text m text s Therefore in this wire the electrons are flowing at the rate of 23 mm s At 60 Hz alternating current this means that within half a cycle on average the electrons drift less than 0 2 mm In context at one ampere around 3 1016 electrons will flow across the contact point twice per cycle But out of around 1 1022 movable electrons per meter of wire this is an insignificant fraction By comparison the Fermi flow velocity of these electrons which at room temperature can be thought of as their approximate velocity in the absence of electric current is around 1570 km s 2 See also EditFlow velocity Electron mobility Speed of electricity Drift chamber Guiding centerReferences Edit Griffiths David 1999 Introduction to Electrodynamics 3 ed Upper Saddle River NJ Prentice Hall p 289 ISBN 9780138053260 http hyperphysics phy astr gsu edu hbase electric ohmmic html Ohm s Law Microscopic View retrieved 2015 11 16External links EditOhm s Law Microscopic View at Hyperphysics Retrieved from https en 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