  Question

# Establish a relation between electric current and drift velocity. OR Prove that the current density of a metallic conductor is directly proportional to the drift speed of electrons.

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Updated on : 2022-09-05
Solution Verified by Toppr

## Relation between electric current and drift velocity.Consider a uniform metallic wire XY of length 1 and cross-sectional area A. A potential difference V is applied across the ends X and Y of the wire.This causes an electric field at each point of the wire of strength.........(i)Due to this electric field, the electrons gain a drift velocity vd opposite to direction of electric field.IF q be the charge through the cross-section of wire in t seconds, then Current in wire ..........(i)The distance traversed by each electron in time t=average velocity x time =vdtIf we consider two planes P and Q at a distance vd in a conductor, then the total charge flowing in time t will be equal to the total charge on the electrons present within the cylinder PQ.The volume of this cylinder =cross sectional area  x heightIf n is the number of free electrons in the wire per unit volume,then the number of free electrons in the cylinder$$=n(Avd t)$$If charge on each electron is ,then the total charge flowing through a cross section of the wire..........(iii) Current flowing in the wire,i.e , current.......(iv)This is the relation between current and drift velocity.Negative sign shows that the direction of current is  opposite to the drift velocityNumericaly ...............(v) Cureent dendity , $$J=\dfrac{t}P{l}{A-}$$\therefgfore)$$Curent density$$J=\dfrac{l}{A}.This is current density of maetallic conductor is directly proportional to the drfyr velocity.   0 0