Derive the relation between Current and drift velocity? Show the current density is directly proportional to drift velocity.
Answers
∴ Total number of electrons in the Conductor = Volume x electron density = Al x n . Under the influence of this field E, free electrons begin to drift in a direction opposite to that of the direction of field. where, vd is the drift velocity of electrons. Thus, current density is proportional to drift velocity.
Answer:
Relation between drift velocity (Vd) and current density(J).
NOW SEE THE 1ST ATTACHMENT
Considered a current carrying conductor of length (l) and area of cross section (A). The free electron density of this conductor be “n” electrons/metre³.
when a potential difference V voltage applied across its end then the electric field E is produced and free electron are move in the direction opposite to the electric field by the drift velocity.
“Drift velocity”: Drift velocity is define as the average velocity with which the electrons get drifted towords positive end of the conductor under the influence of an external electric field. it is denoted by Vd.
Thus, Vd = l/t = (U+V)/2
The Free electron density of a conductor be “n” electrons/metre ³.
i.e 1m³ volume containing = n free electron
Hence,
(AL) m³ Volume containing (N) = n.(AL) electrons
Thus, amount of charge flows through any cross section of a conductor,Q = N.e We know that
Current, I = Q/t
Hence, I = ( .e)/t
I = n.e.A(l/t)
{By the definition
Drift velocity,Vd = l/t }
I = n.eA(Vd)
And current density, J = I/A
J = (n.e.A.Vd)/A
J = n.e.Vd
Here the quantity (n.e) is constant term
Hence, [ J ∝ Vd ]
Thus the current density of a current carrying conductor is directly proportional to the Drift velocity of free electron.
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