A solid wire with a radius of 10 cm carries a 5.0 A current that is uniformly distributed across its cross section. Determine the magnetic field B at a point located at a distance of 10 cm from the axis.

Step-by-step solution

Using Ampere's circuital law, the magnetic field at a distance r from the axis of a solid cylindrical wire of radius R carrying current I is given by B = ₀ I 2 r for r R . Here, the point is at a distance r = 10 cm = 0.1 m , which is exactly on the surface of the wire ( R = 10 cm ). Substituting the given values: B = 4 10⁻⁷ 5.0 2 0.1 B = 2 10⁻⁷ 5.0 0.1 B = 100 10⁻⁷ T B = 10 10⁻⁶ T = 10 T