Question

2.21P) A cylindrical wire along x axis, that carries a current, consists of three sections with different radius (1A, 1B, 1C). In figure it shown that the voltage change along the wire length. Rank the each section according to the following quantities, greatest first: a) current, b) magnitude of current density, and c) magnitude of electric field. (Show first your result than your calculation clearly) TABIC

Answer 1

The answers are

a)

1A = ig=id

b)

JA Ja

c)

Ев EA > Ed

a) The current through all the three segments is same.

1A = ig=id

b) The relation between potential difference and current is
AL V = iR
;
ρL ΔV = 1
;

  
AV = P pЈ 1
=>
Ja 1

The current density is proportional to the slope of Potential and length graph.

If the slope is more then the current density is more. The slope is greatest for segment B and least for segment C.

Hence

JA Ja

c)
=σΕ
where $\sigma$ is conductivity which is constant for all the three segments.

Hence electric field is directly proportional to current density. Then

ER EA > Ed