I was amazed to see how my car's tire started attracting the nuts and bolts, how in the world did it induce the magnetic field? Never heard of such phenomena!!!
[Physics] How does the magnetic field get induced in car’s tire
electromagnetismelectrostaticseveryday-lifemagnetic fields
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Yes, of course that if a field - magnetic field - is able to make a bar magnet rotate or move, it is doing work. The statement that magnetic fields don't do any work only applies to point-like pure electric charges.
Magnetic moments may be visualized as objects with a forced motion of charges (solenoids have the same magnetic field as bar magnets), and if something is moving, the magnetic force is becoming a force that does work.
In terms of formulae, the magnetic force on a charge is $q\vec v\times \vec B$ which is identically perpendicular to $\vec v$ and that's why it does no work. However, forces on magnetic dipoles and more general objects don't have the form $\vec v\times$ - they're not perpendicular to $\vec v$, so they do work in general.
Time-varying means that as time, $t$, increases, the magnetic field changes. One of the more common representations is a sinusoidal wave:
(image from the linked Wikipedia page). Though the image above says $x$, the relation between $x$ and $\sin(x)$ is what is important.
With magnetic fields, Maxwell's equations, $$ \nabla\cdot\mathbf E=\frac\rho{\epsilon_0} \quad \nabla\cdot\mathbf B=0 \\ \nabla\times\mathbf E=0 \quad \nabla\times\mathbf B=\mu_0\mathbf J $$ (where $\mathbf E$ is the electric field, $\mathbf B$ the magnetic field, $\mathbf J$ the current density, $\epsilon_0$ the vacuum permittivity, $\rho$ the charge density, and $\mu_0$ the vacuum permeability) then become $$ \nabla\cdot\mathbf E=\frac\rho{\epsilon_0} \quad \nabla\cdot\mathbf B=0 \\ \nabla\times\mathbf E=\color{blue}{-\frac{\partial\mathbf B}{\partial t}} \quad \nabla\times\mathbf B=\mu_0\mathbf J+\color{blue}{\frac{1}{c^2}\frac{\partial\mathbf E}{\partial t}} $$ where the blue-colored terms show that the two fields induce each other when changing in space and/or time.
Best Answer
Car tyres, which these days are almost always radials, are sometimes reinforced with steel. It may be possible that these have become magnetized due to impact in the Earth's field, although I find that unlikely unless you constantly drive in one direction.
Otherwise, maybe someone has run a magnet over your tyres?
Adding quotes from another paper on the subject