Chapter 27, Problem 27.51P

When a particle of charge q > 0 moves with a velocity of ${\stackrel{\to }{\upsilon }}_1$ at 45.0° from the +x-axis in the xy-plane, a uniform magnetic field exerts a force ${\stackrel{\to }{\text{F}}}_1$ along the -z-axis (Fig. P27.51). When the same particle moves with a velocity ${\stackrel{\to }{\upsilon }}_2$ with the same magnitude as ${\stackrel{\to }{\upsilon }}_1$ but along the +z-axis, a force ${\stackrel{\to }{\text{F}}}_2$ of magnitude F₂ is exerted on it along the +x-axis. (a) What are the magnitude (in terms of q, ʋ₁, and F₂) and direction of the magnetic field? (b) What is the magnitude of ${\stackrel{\to }{\text{F}}}_1$ in terms of F₂?

Figure P27.51