Current Density MCQ - Practice Questions with Answers

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

At point $P$ :
$j=\underset{\mathrm{\Delta }A\to 0}{lim}\frac{\mathrm{\Delta }i}{\mathrm{\Delta }A}$ in the direction of current
2. If current not Perpendicular to Area

$\begin{array}{rl}& J_{av}=\frac{di}{dA\cos \theta }\\ & di=JdA\cos \theta =\overrightarrow{J}\cdot d\overrightarrow{A}\end{array}$

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

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

- Unit and dimension -

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