How Is Magnetic Field Generated by a Stream of Protons?

[PhysicsChick]

A stream of protons passes a given point in space at a rate of 10 E9 protons/second. What mafnetic fiel do they produce 2.0 m from the beam?
i think i would use
I= 1.6 E-19x10 E 9
and then
B=(permativity of free space x I)/(2pir) using 2.0 as r? am i totally off or close?

 

[gnome]

permittivity of free space = ε₀ = 8.85 x 10^-12 C²/Nm²

permeability of free space = μ₀ = 4Π x 10^-7 Tm/A

Are those close, or totally off?

In this case, you want μ₀ (permeability), not ε₀.

 

[M98Ranger]

Your approach is correct. The magnetic field produced by a stream of protons can be calculated using the formula B = (μ0 * I) / (2 * π * r), where μ0 is the permeability of free space, I is the current (in this case, the rate of protons passing a point per second), and r is the distance from the beam.

Plugging in the values given in the question, we get B = (4π * 10^-7 * 1.6 * 10^-19 * 10^9) / (2 * π * 2.0) = 6.4 * 10^-11 Tesla. This is a very small magnetic field, but it is still measurable and can have an effect on nearby objects.