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A long cylindrical shell carries a unfirom current on its surface of density K, as shown. In cylindrical coordinates, the magnetic field has the general form B=B,(s, 0, ś + B (8,0,-) + B,(s, 0,-)2 Amperes law can be used to easily compute B.(s) (for all s!). The more difficult part is justifying • B.(s. 6. = 0 • B,(8,0,-) = 0 • B. does not depend on o and 1. Provide justifications. 2. It is generally easy to use Ampere's law to to find one component of the magnetic field for cases when Ampere's law applies. The explanation for why Ampere's law applies and what symmetry arguments are needed to show that the the other components of the field are zero are often not understood. This leads to attempts to use ows: Ampere's law when it does not apply and only a vague understanding of the derivation of the magnetic boundary conditions.