Near Earth, the density of protons in the solar wind (a stream of particles from the Sun) is 11.6 cm-3, and their speed is 563 km/s. (a) Find the current density of these protons. (b) If Earth's magnetic field did not deflect the protons, what total current Earth receive?

a) 10462341.6*10⁻¹³ A/m²

b) 133709238.907 A

Explanation:

n = Density of the protons in the solar wind = 11.6 cm⁻³ = 11.6*10⁶ m⁻³

v = Velocity of the protons = 563 km/s = 563000 m/s

e = Charge of a proton = 1.602*10⁻¹⁹ coulombs

R = Radius of Earth = 6.3781*10⁶ m

A = Area of Earth = πR² = π (6.3781*10⁶) ²=127.8*10¹² m²

a) Current density

J = nev

⇒J = 11.6*10⁶*1.602*10⁻¹⁹*563000

⇒J = 10462341.6*10⁻¹³ A/m²

∴ Current density of these protons is 10462341.6*10⁻¹³ A/m²

b) Current

I = JA

⇒I = 10462341.6*10⁻¹³*127.8*10¹²

⇒I = 1337092389.07*10⁻¹

⇒I = 133709238.907 A

∴ Total current Earth receives is 133709238.907 A