Your work looks right to me.gausswell said:
A surface current on a spherical superconductor refers to the flow of electric charge that occurs on the surface of the superconducting material. In superconductors, these currents can flow without resistance, allowing for the maintenance of a persistent current on the surface.
The Meissner effect causes a superconductor to expel magnetic fields from its interior, leading to the establishment of surface currents that generate a magnetic field opposing the applied field. This results in the magnetic field being confined to a thin layer at the surface, often referred to as the London penetration depth.
The distribution of surface currents on a spherical superconductor is determined by the external magnetic field configuration and the geometry of the superconductor. The currents arrange themselves in such a way as to cancel the internal magnetic field, conforming to the spherical symmetry of the object.
Direct measurement of surface currents on a spherical superconductor is challenging due to the non-invasive nature required to preserve superconductivity. However, indirect methods such as measuring the magnetic field distribution outside the superconductor or using SQUID (Superconducting Quantum Interference Device) magnetometers can provide insights into the surface current distribution.
Understanding surface currents in spherical superconductors has applications in various fields including magnetic shielding, quantum computing, and medical imaging technologies like MRI. The ability to control and manipulate these currents can lead to advancements in designing superconducting materials and devices with specific magnetic properties.