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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?

Respuesta :

Answer:

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

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