Charge Velocity and Velocity of Field Propagation

The speed with which charge drifts in a conductor is called the velocity of charge. As seen from page Electron Drift Velocity . its value is quite low, typically fraction of a metre per second.

However. the speed with which the effect of e.m.f. is experienced at all parts of the conductor resulting in the flow of current is called the velocit.v of propagation of electri8calfield. It is independent of current and voltage and has high but constant value of nearly  $3\times {10}^{8}m/s^{\mathrm{}}$.

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Example

Find the velocity of charge leading to 1 A current which flows in a copper conductor of cross-section 1 ${\mathrm{cm}}^2$ and length 10 km. Free electron density of copper $\mathrm{= \; 8.5}\times {10}^{28}{}^{\mathrm{}}$per $m^3$. How long will it take the electric charge to travel from one end of the conductor to the other.

Solution

                i = neAv  or v = i / neA

     so,      v=18.5×1028×(1.5×1019)×(1×10-4) =7.35×10-7 m/s =0.735 μm/s

Time taken by the charge to travel conductor length of 10 km is,

t=distancevelocity=10×1037.35×10-7=1.36×1010 second

Now. 1 year = 365 x 24 x 3600 = 31,536.000 s

           so, t =1.36×1010/31,53,6000 = <b>431</b>years

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