Chapter 28, Problem 10P

(II) A straight stream of protons passes a given point in space at a rate of 2.5 × 10⁹ protons/s. What magnetic field do they produce 2.0 m from the beam?

The stream of proton constitutes a current, whose magnitude is found by multiplying the proton rate times the charge of proton. Then use Eq. 28-1 to calculate the magnetic field.

$B_{\text{stream}}=\frac{{\mu }_{0}I}{2\pi r}=\frac{\left(4\pi \times {10}^{-7}\text{T}\cdot \text{m/A}\right)\left(2.5\times {10}^9\text{protons/s}\right)\left(1.60\times {10}^{-19}\text{C/proton}\right)}{2\pi (2.0\text{m})}=\boxed{4.0\times {10}^{-17}\text{T}}$