Question

A copper wire has a square cross section 2.3 mm on a side. The wire is 4.0 m long and carries a current of 3.7 A . The density of free electrons is 8.5×10²⁸ m⁻³. Find the magnitude of the current density in the wire.

Answer 1

To find the current density of the copper wire, calculate the cross-sectional area using the side length and then apply the formula J = I/A with the provided current value.

Step-by-step explanation:

The question is asking to find the magnitude of the current density in a wire with a square cross-sectional area. Current density (J) is defined as the electric current (I) flowing per unit area (A) of a material, which can be mathematically represented as J = I/A.

To find the current density, we first calculate the cross-sectional area of the wire. Since the wire has a square cross section, we can calculate the area as A = side × side, where the side length is 2.3 mm, or 2.3 × 10-3 m given in SI units.

Detailed Steps to Calculate Current Density:

By performing the arithmetic, we obtain the current density for the given wire.