Ranking Current Densities: How Do Different Factors Affect Current Flow?

[DottZakapa]

Homework Statement

Rank in order, from the largest to the smallest, the current densities in these four wires, that have different radius and different electric conductivity

Relevant Equations

current density resistivity and resistance i guess

Homework Statement: Rank in order, from the largest to the smallest, the current densities in these four wires, that have different radius and different electric conductivity
Homework Equations: current density resistivity and resistance i guess

j_a=I/πr²
j_b=2I/πr²
j_c=I/2πr²

J_b > j_a > j_c ...

i don't get how to use 2σ in order to find and compare the current density of d.
I know that
ρ=L/σπr² but ...

 

[Doc Al]

i don't get how to use 2σ in order to find and compare the current density of d.

Do the same analysis as you did for a, b, and c. (Is the conductivity relevant?)

 

[DottZakapa]

not taking care of it the result is correct, but could you briefly explain why is not relevant ? Does it becomes relevant only for the potential difference ?

 

[Doc Al]

Don't overthink what they are asking for: The current density is current/cross-sectional area. The current is given in each case!

For a different question, the conductivity can be relevant. For example, the electric field strength within the conductor would depend on the conductivity. (But they didn't ask that here.)

 

[DottZakapa]

ok thanks very gentle

 

[Tom.G]

current/surface area.

current/Cross Sectional area.

 

[Doc Al]

current/Cross Sectional area.

Oops! Thanks, @Tom.G; I'll correct that.