An infinitely long hollow conducting cylinder with inner radius R / 2 and outer radius R carries a uniform current density along its length. The magnitude of the magnetic field, B as a function of the radial distance r from the axis, is bes

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An infinitely long hollow conducting cylinder with inner radius R / 2 and outer radius R carries a uniform current density along its length. The magnitude of the magnetic field, B as a function of the radial distance r from the axis, is best represented by

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The required cylinder is shown in figure Let j = current density, then For, r < R 2 B = 0 For, R 2 ≤ r ≤ R B × 2 πr = μ 0 jπ r 2 - R 2 4 B = μ 0 j 2 r - R 2 4 r For, r > R B × 2 πr = μ 0 jπ R 2 - R 2 4 B = μ 0 j 2 ⋅ 2 R 2 4 r ⇒ B ∝ 1 / r [this is an equation for rectangular hyperbola.]

An infinitely long hollow conducting cylinder with inner radius R / 2 and outer radius R carries a uniform current density along its length. The magnitude of the magnetic field, B as a function of the radial distance r from the axis, is best represented by

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