Hi Thien,
There are different kinds of solar storms. I am thinking you mean coronal mass ejections (CMEs). These are giant clouds that blast off the sun and out into the solar system. They are large, but they have very low density, so it is reasonable to wonder how they affect things at Earth. They do this because they bring along a part of the Sun's magnetic field, which interacts with Earth's magnetic field. That effect on the Earth's magnetic field is what caused the Northern and Southern lights and also can cause problems with power systems and communications.

Without Earth's magnetic field, though, the effects in the long term might be even greater. One of the things the MAVEN mission to Mars is studying is the effect of CMEs and the solar wind on the Martian atmosphere. Mars has a much smaller magnetic field and one idea is that CMEs and the solar wind may have affected Mars's atmosphere over the years - making it a much more desert-like place. There is more about that here:
https://www.nasa.gov/cont...ss-ejections-at-mars