Magnetic Field Produced by Straight Currents Video Lessons

Concept

# Problem: A 2.4 mm-diameter copper wire carries a 30 A current (uniform across its cross section).a) Determine the magnetic field at the surface of the wire.b) Determine the magnetic field inside the wire, 0.50 mm below the surface.c) Determine the magnetic field outside the wire 2.5 mm from the surface.

###### FREE Expert Solution

Magnetic field around a wire carrying current:

$\overline{){\mathbf{B}}{\mathbf{=}}\frac{{\mathbf{\mu }}_{\mathbf{0}}\mathbf{i}}{\mathbf{2}\mathbf{\pi }\mathbf{r}}}$, where i is current, r  is the radius of the wire, and μ0 is the permeability of free space.

μ0 = 4π × 10-7T•m/A

The diameter of the copper wire, d = 2.4 mm

The radius, r = d/2 = 2.4/2 = 1.2 mm = 1.2 × 10-3 m

a)

The magnetic field at the surface of the copper wire is:

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###### Problem Details

A 2.4 mm-diameter copper wire carries a 30 A current (uniform across its cross section).
a) Determine the magnetic field at the surface of the wire.
b) Determine the magnetic field inside the wire, 0.50 mm below the surface.
c) Determine the magnetic field outside the wire 2.5 mm from the surface.