A current of 2 ampere is passing in an aluminium wire whose cross-section is `4xx10^(-3)m^2`
The value of current density in `(A//m^2)` is:

Options

A. `2xx10^2Am^(-2)`
B. `5xx10^2Am^(-2)`
C. `4xx10^2Am^(-2)`
D. None of these

Explanation

To find the current density in the aluminium wire, we can use the formula for current density (J):

\[ J = \frac{I}{A} \]

where:
- \( J \) is the current density (in A/m²),
- \( I \) is the current (in amperes),
- \( A \) is the cross-sectional area (in m²).

### Step 1: Identify the given values
From the question, we have:
- Current, \( I = 2 \, \text{A} \)
- Cross-sectional area, \( A = 4 \times 10^{-3} \, \text{m}^2 \)

### Step 2: Substitute the values into the formula
Now, we substitute the values of current and area into the current density formula:

\[ J = \frac{2 \, \text{A}}{4 \times 10^{-3} \, \text{m}^2} \]

### Step 3: Perform the calculation
Calculating the above expression:

1. First, divide the current by the area:

\[ J = \frac{2}{4 \times 10^{-3}} \]

2. Simplifying \( \frac{2}{4} \):

\[ J = \frac{1}{2} \times \frac{1}{10^{-3}} \]

3. Since \( \frac{1}{10^{-3}} = 10^{3} \):

\[ J = 0.5 \times 10^{3} \]

4. Converting \( 0.5 \) to scientific notation:

\[ J = 5 \times 10^{2} \, \text{A/m}^2 \]

### Step 4: State the final answer
Thus, the current density in the aluminium wire is:

\[ J = 5 \times 10^{2} \, \text{A/m}^2 \]