Space Physics (sun and solar wind) problem

[jdup21]

Homework Statement

If, (average solar wind properties at Earth's orbit)
Proton density = 7 cm^-3 flow speed=400km/s almost radial
electron density=7.5 cm^-3, proton temp=2*10^5 Kelvin
He^2+ density= .25 cm^-3 electron temp=1*10^5 Kelvin
Magnetic field=7nT

Find flux through sphere and flux densities of radius 1AU for: protons, thermal energy, magnetic energy, radial magnetic flux, kinetic energy, radial momentum, and mass

Homework Equations

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The Attempt at a Solution

Attempted many times and not getting very far.. a start on the problem will be greatly appreciated

-Thanks!

 

[mark726]

Hello,

Thank you for your post. Let's start by defining some equations that will be useful for solving this problem:

1. Flux: Flux is defined as the amount of a physical quantity passing through a given area per unit time. It is represented by the symbol Φ and is given by the equation Φ = ∫B⋅dA, where B is the magnetic field and dA is the differential area.

2. Flux density: Flux density is defined as the amount of flux passing through a unit area. It is represented by the symbol B and is given by the equation B = Φ/A, where Φ is the flux and A is the area.

3. Radius of 1AU: 1 AU (astronomical unit) is defined as the average distance between the Earth and the Sun, which is approximately 1.496×10^8 km.

Now, let's use these equations to find the flux through a sphere of radius 1AU and the flux densities at this radius for the given parameters:

1. Flux through sphere: The flux through a sphere of radius 1AU can be calculated by integrating the magnetic field over the entire surface of the sphere. Since the magnetic field is almost radial, we can simplify this equation to Φ = B*A, where B is the magnetic field and A is the surface area of the sphere. The surface area of a sphere is given by A = 4πr^2, where r is the radius. Plugging in the values, we get Φ = (7nT)*(4π*(1.496×10^8 km)^2) = 4.189×10^18 nT*km^2.

2. Flux density for protons: To find the flux density for protons, we need to find the flux passing through a unit area. Since we already know the total flux through the sphere, we can simply divide it by the surface area of the sphere. This gives us B = Φ/A = (4.189×10^18 nT*km^2)/(4π*(1.496×10^8 km)^2) = 7.47×10^-8 nT*km^-2.

3. Flux density for thermal energy: The flux density for thermal energy can be calculated using a similar approach as above. We know that the thermal energy is proportional to the temperature, so we can simply use the