A long straight solid cylindrical conductor of radius R carries a steady current uniformly distributed over its cross-section. The magnitude of the magnetic field at a radial distance x (where x R ). Which of the following relations is correct?

Step-by-step solution

For a solid cylindrical conductor carrying a uniform current I , the magnetic field at a distance r from the axis is given by: Inside the conductor ( r B_ in = ₀ I r 2 R^2 Outside the conductor ( r > R ): B_ out = ₀ I 2 r Given that the magnetic field at distance x ( x R ), we can equate the two expressions: ₀ I x 2 R^2 = ₀ I 2 y Cancelling the common terms ₀ I 2 from both sides, we get: x R^2 = 1 y Rearranging the terms yields: xy = R^2 Answer: xy = R^2