Chapter 30, Problem 30.65AP

As seen in previous chapters, any object with electric charge, stationary or moving, other than the charged object that created the field, experiences a force in an electric field. Also, any object with electric charge, stationary or moving, can create an electric field (Chapter 22). Similarly, an electric current or a moving electric charge, other than the current or charge that created the field, experiences a force in a magnetic field (Chapter 28), and an electric current creates a magnetic field (Section 29.1). (a) To understand how a moving charge can also create a magnetic field, consider a particle with charge q moving with velocity $\stackrel{\to }{v}$. Define the position vector $\stackrel{\to }{r}=r\hat{r}$ leading from the particle to some location. Show that the magnetic field at that location is

$\stackrel{\to }{B}=\frac{{\mu }_0}{4\pi }\frac{q\stackrel{\to }{v}\times \hat{r}}{r^2}$

(b) Find the magnitude of the magnetic field 1.00 mm to the side of a proton moving at 2.00 × 10⁷ m/s. (c) Find the magnetic force on a second proton at this point, moving with the same speed in the opposite direction. (d) Find the electric force on the second proton.