Question

Two conducting wires of conductivity ${\sigma }_1$ and ${\sigma }_2$ having same cross-section area are connected end to end as shown in figure. This composite wire carry current I, then

• A. junction of wires has some positive charge if ${\sigma }_1$> ${\sigma }_2$.
• B. junction of wires has some negative charge if ${\sigma }_1$> ${\sigma }_2$.
• C. charge at junction is $\left(\frac{{\epsilon }_{0}I({\sigma }_1-{\sigma }_2)}{{\sigma }_1{\sigma }_2}\right|$.
• D. electric field is same in both wires.

Answer 1

Answer: (A), (C)

The correct options are
A junction of wires has some positive charge if ${\sigma }_1$> ${\sigma }_2$.
C charge at junction is $\left(\frac{{\epsilon }_{0}I({\sigma }_1-{\sigma }_2)}{{\sigma }_1{\sigma }_2}\right|$.


In a steady state of current flow, the normal component of the current density J must be the same on both sides of the junction
$J_1=J_2{\sigma }_1{E}_1={\sigma }_2{E}_{2}if{\sigma }_1>{\sigma }_2,then{E}_2>E_{1}Toincreasefieldinregionof{\sigma }_{2}weneedpositivechargeatjunction.ByGausslaw,\frac{Q}{{\epsilon }_0}=(E_2-E_1)AQ={\epsilon }_{0}A(\frac{J}{{\sigma }_2}-\frac{J}{{\sigma }_1})\Rightarrow Q=\frac{{\epsilon }_{0}I({\sigma }_1-{\sigma }_2)}{{\sigma }_1{\sigma }_2}$