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 `Am^-2`

Options

A. 0.5
B. 1
C. `10`
D. `3//10`

Answer

To find the current density \( J \) in a conductor, 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 cross-sectional area in square meters (m²).

**Step 1: Convert the current from microamperes to amperes.**

Given:
- Current \( I = 50 \, \mu A = 50 \times 10^{-6} \, A \)

**Step 2: Convert the area from square millimeters to square meters.**

Given:
- Area \( A = 50 \, mm^2 = 50 \times 10^{-6} \, m^2 \)

**Step 3: Substitute the values into the formula for current density.**

Now we can substitute the values of \( I \) and \( A \) into the formula:

\[ J = \frac{50 \times 10^{-6} \, A}{50 \times 10^{-6} \, m^2} \]

**Step 4: Simplify the expression.**

\[ J = \frac{50}{50} \, A/m^2 = 1 \, A/m^2 \]

Thus, the value of the current density \( J \) is:

\[ J = 1 \, A/m^2 \]

### Final Answer:
The current density in the conductor is \( 1 \, A/m^2 \).

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