Question

1 Obtain the relation between the drift velocity V. and relaxation timer of the free electrons in a
conductor in the presence of applied electric field E Hence show that the current density Jis
directly proportional to electric field where proportionality constant o =ne t/m denotes the
conductivity of the material of the conductor and n is the number density of Free electrons (5)​

Answer 1

Answer:

We knew the EQ of (drift velocity) I. e Vd=(e ×E ×torque) /m.( EQ of vd)

We also know (current density) j=I/A ( EQ A)

For finding I(current) =

Total no. Of electron per unit volume=e × A×L

=>e × A ×Vd×T. (L=Vd×T) -(eqi)

Total charge =n×e(by putting EQ I)

=>n ×e. A. Vd. T -EQ ii

We know I=Q/T

Put valu e of EQ ii

I=(n. e. A. Vd. T) /T

I=n. e. A. Vd

Put value of I in EQ A

J=I/A

J=(n. e. A. Vd) /A

Then j=n. e. Vd

Now put the value of vd.

J=(n × e ×e × E ×torque) /m

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