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Abstract In this paper, viscous incompressible hydromagnetic flow around a sphere has been investigated by considering the penetration of the magnetic field inside it. Earlier researchers have found it difficult because it not only adds an extra equation to the system of governing equations but also needs a proper matching of the components of the magnetic fields at the interface. However, using a higher‐order compact finite difference scheme, we have successfully solved the governing highly nonlinear and coupled system of partial differential equations and have obtained converged solutions throughout the domain of the parameter space. In this novel numerical investigation, we have calculated the magnetic field throughout the whole domain, that is, both inside the sphere and within the fluid, with a suitable matching at the interface–a feature that has allowed us to capture the actual interactions occurring between the fluid flow and the magnetic field and unfurl several new characteristics of scientific and technological value. In fact, we have found that the magnetic field penetrating inside the sphere can effectively cause the critical value of Reynolds number to increase and can help to suppress flow separation more effectively than otherwise.