A long cylindrical conductor of length carries a steady current

PHYSICS · Subjective · CBSE · Physics · Current Electricity · Current Electricity

Problem

A long cylindrical conductor of length

L

carries a steady current

I

. The radius of the conductor is not uniform but varies linearly with distance

x

from one end according to

r(x)=r_{0}\left(1+\dfrac{x}{L}\right)

, where

0\le x\le L

. (a) Derive an expression for the drift velocity

v_{\!d}(x)

of free electrons as a function of

x

, assuming the number density of charge carriers

n

is constant along the conductor. (b) Using your result from part (a), obtain an expression for the average drift velocity

\langle v_{\!d}\rangle

over the entire length

L