A long straight solid wire of radius R carries a steady current uniformly distributed across its cross-section. The magnitude of the magnetic field at a radial distance x from the axis (where x R ). The radius R of the wire can be expressed as:

Step-by-step solution

Let the uniform current in the solid wire be I . The magnetic field at a point inside the wire at a radial distance x ( x B_ in = ₀ I x 2 R^2 The magnetic field at a point outside the wire at a radial distance y ( y > R ) is given by: B_ out = ₀ I 2 y Given that the magnitudes of the magnetic fields at these two points are equal: B_ in = B_ out ₀ I x 2 R^2 = ₀ I 2 y Cancelling the common terms ₀ I 2 on both sides: x R^2 = 1 y Rearranging to solve for R : R^2 = xy R = xy Answer: xy