A conductor-carries a current of `50 muA` If the area of cross-section of the conductor is `50 mm^(2)`, then value of the current density in Amis

Options

A. 0.5
B. 1
C. `10_(1)`
D. `3//10`

Answer

To find the current density (J) in a conductor carrying a current (I), we can use the formula:

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

where:
- \( J \) is the current density in Amperes per square meter (A/m²),
- \( I \) is the current in Amperes (A),
- \( A \) is the area of cross-section in square meters (m²).

### Step-by-Step Solution:

1. **Identify the given values**:
- Current, \( I = 50 \, \mu A = 50 \times 10^{-6} \, A \)
- Area of cross-section, \( A = 50 \, mm² = 50 \times 10^{-6} \, m² \) (since \( 1 \, mm² = 10^{-6} \, m² \))

2. **Convert the area to square meters**:
\[ A = 50 \, mm² = 50 \times 10^{-6} \, m² \]

3. **Substitute the values into the formula for current density**:
\[ J = \frac{I}{A} = \frac{50 \times 10^{-6} \, A}{50 \times 10^{-6} \, m²} \]

4. **Simplify the expression**:
\[ J = \frac{50}{50} \times \frac{10^{-6}}{10^{-6}} = 1 \, A/m² \]

5. **Final Result**:
The current density \( J \) is \( 1 \, A/m² \).