As far as I understand it, the Earth's magnetic field rotates around the planet's axis at the same rotational velocity as the planet's rotational velocity around its axis.
From what I understand about the interaction of a magnetic field and charged particles, the velocity of a moving magnetic field is a factor in how well a magnetic field will deflect/redirect charged particles that enter into it.
So, if the Earth's rotational velocity around its axis was faster, and say that this reduced the length of a day down to 22 hours, the Earth's magnetic field would then be moving faster and it should be more effective at deflecting/redirecting charged particles in the Sun's solar wind.
I am not a physicist or a scientist. I am asking this question simply out of scientific curiosity.
Would the Earth's magnetosphere be more effective against the Sun's solar wind if the planet's rotation was faster?