Current Density - Practice Questions & MCQ

1.  Current density

• Current density: The amount of electric current flowing per unit cross-sectional area of a material.

• It is a vector quantity.

If a current of $\Delta i$ flows through an area $\Delta A$ the average current density $\bar{j}=\frac{\Delta i}{\Delta A}$ in the direction of current

At point $P$ :
$j=\lim _{\Delta A \rightarrow 0} \frac{\Delta i}{\Delta A}$ in the direction of current

2. If current not Perpendicular to Area

$
\begin{aligned}
J_{a v} & =\frac{d i}{d A \cos \theta} \\
d i & =J d A \cos \theta=\vec{J} \cdot d \vec{A}
\end{aligned}
$

$\theta$ is the angle between the normal to the area and direction of current
- If the current density $\vec{J}$ is uniform for a normal cross-section $\vec{A}$ then

$
i=\int \vec{J} \cdot d \vec{A}
$

- Unit and dimension -

Unit of current density is $A \mathrm{mp} / \mathrm{m}^2$
DImension of current density is $\left[L^{-2} A\right]$