# Why in superconducting cylindrical thin tube of radius $R$ the magentic field lines would be exactly parallel to the axis of cylinder?

Consider a superconducting cylindrical coil of length $$L$$ radius $$R$$ and having a current I around its mantle, (Assume that current causes magentic field which passes through the superconductor area at T>Tc(critical temperature for superconductor) after that its switches to T<Tc so that field lines still are there inside) Now my question: why its true that the field lines inside the cylinder would always be parallel to the axis and if its true why it will be uniform also just in case it also happens? What can we say regarding outside field? If its zero outside why is it so? And whats the difference in this and a solenoid of same length L and radius R in terms of magnetic fields at various locations? Is there no approximation being made in case of the former one while calculating any field as such (i.e there is no edge effects at all in former etc.)? Setup consists of just a superconducting cylinder and somehow the current is flowing outside of cylinder in helical pattern around thee cylindrical surface, if length ,radius are comparable , even then we observe that field value is is always uniform inside why ? (This "current passing setup" was done so as to calculate the self inductance of the superconducting cylinder)

• Sorry, I do not understand the geometry of the system. Are you considering a full cylinder of superconducting material, a superconducting cylindrical shell or a solenoid made with a coil of superconducting material? What is the "mantle"? Feb 22, 2022 at 21:52
• Mantle means the curved surface of cylinder where current is moving around in helical but nearly many circlular loops and yes i am considering a full cylinder of superconducting material . Lastly i was referring to difference between this and normal solenoid . In terms of magnetic field lines and other stuffs Feb 22, 2022 at 22:36
• if your superconducting material is type 1 then you can do the "field cooling". You impose a certain uniform B outside the sample in its normal state, along the axis of rhe cylinder. You cool down rhe sample, at B constant. Then you go below the transition temperature the same becomes superconducting: persistent surface currents will develop on the cylindrical surface (circulating around the axis of the cylinder) that shield the B from the interior (Meissner effect). Feb 22, 2022 at 23:49
• Feb 22, 2022 at 23:52
• Its a bit different @Quillo , i am asking for a cylinder (superconducting ) in which a current is flowing in a helical patttern on the curve surface , my question was inside field value will be uniform , why that is what i am asking . (Nothing more is present there ) Feb 28, 2022 at 10:35