What do you mean by "deep"? Most of the solar wind is deflected by the Earth's magnetic field:Mikael17 said:How many particles (approximately) from the solar wind reach deep into the Earth's magnetic field every second. Possibly measured in mass?
https://www.jpl.nasa.gov/nmp/st5/SCIENCE/solarwind.htmlWhen the solar wind encounters Earth, it is deflected by our planet's magnetic shield, causing most of the solar wind's energetic particles to flow around and beyond us. This region that meets and blocks the solar wind is called the magnetosphere.
https://en.wikipedia.org/wiki/Solar_windVelocity and density
Near the Earth's orbit at 1 astronomical unit (AU) the plasma flows at speeds ranging from 250 to 750 km/s with a density ranging between 3 and 10 particles per cubic centimeter and temperature ranging from 104 to 106 Kelvin.[45]
On average, the plasma density decreases with the square of the distance from the Sun, see Section 4.2,[46] while the velocity decreases and flattens out at 1 AU, see Figure 5.[46]
Voyager 1 and Voyager 2 reported plasma density n between 0.001 and 0.005 particles/cm3 at distances of 80 to 120 AU, increasing rapidy beyond 120 AU at Heliopause to between 0.05 and 0.2 particles/cm3.[47]
Pressure
At 1 AU, the wind exerts a pressure typically in the range of 1–6 nPa ((1–6)×10−9 N/m2),[48] although it can readily vary outside that range.
The ram pressure is a function of wind speed and density. The formula is
P = m p ⋅ n ⋅ V 2 = 1.6726 × 10 − 27 k g ⋅ n ⋅ V 2 {\displaystyle P=m_{\text{p}}\cdot n\cdot V^{2}=\mathrm {1.6726\times 10^{-27}\,kg} \cdot n\cdot V^{2}}
where mp is the proton mass, pressure P is in Pa (pascals), n is the density in particles/cm3 and V is the speed in km/s of the solar wind.[49]