First slide

current density

Question

A current I flows through a cylindrical rod of uniform cross-sectional area A and resistivity $ρ$ . The electric flux through the shaded cross-section of rod as shown in figure is:

Moderate

A

$\frac{I}{ρ}$
B

$ρI$
C

$\frac{ρI}{A}$
D

$\frac{ρA}{I}$

Solution

The current density J, electric field E at the cross-section are related by $J = \frac{E}{ρ}$
Multiplying both side by A, we get
$\begin{array}{l} JA = \frac{EA}{ρ} or I = \frac{ϕ}{ρ} where ϕ is electric flux . \\ or ϕ = ρI \end{array}$

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