Question

An electric field of 0.01 V/m is applied along the length of a copper wire of circular cross-section with diameter 1 mm. Copper has a conductivity of \( 5.8 \times 10^7 \, {S/m} \). The current (in Amperes, rounded off to two decimal places) flowing through the wire is _________.

• A. 0.46
• B. 1.82
• C. 0.58
• D. 1.12

Hint:

To calculate the current in a conductor, use the formula \( I = J \cdot A \), where \( J = \sigma E \) and \( A \) is the cross-sectional area. Be careful with unit conversions, especially for area and electric field.

Answer 1

The Correct Option is A

The current \( I \) through the wire can be calculated using Ohm's law: \[ I = J \cdot A \] where:
\( J \) is the current density, and
\( A \) is the cross-sectional area of the wire.
The current density \( J \) is related to the electric field \( E \) and conductivity \( \sigma \) as: \[ J = \sigma E \] The cross-sectional area \( A \) of the wire is: \[ A = \pi r^2 \] where \( r \) is the radius of the wire. Given that the diameter is 1 mm, the radius \( r \) is 0.5 mm or \( 0.5 \times 10^{-3} \, {m} \). Substituting the given values:
Conductivity \( \sigma = 5.8 \times 10^7 \, {S/m} \),
Electric field \( E = 0.01 \, {V/m} \),
Radius \( r = 0.5 \times 10^{-3} \, {m} \).
First, calculate the current density: \[ J = (5.8 \times 10^7) \cdot 0.01 = 5.8 \times 10^5 \, {A/m}^2 \] Next, calculate the area of the wire: \[ A = \pi (0.5 \times 10^{-3})^2 = 7.854 \times 10^{-7} \, {m}^2 \] Finally, calculate the current: \[ I = (5.8 \times 10^5) \cdot (7.854 \times 10^{-7}) = 0.46 \, {A} \] Thus, the correct answer is 0.46 A.