The magnetic field of an electromagnetic wave is B⃗=B₀(î+ĵ)/√2 cos(kz-ωt). At t=0, charges q₁=4π C at z=π/k and q₂=2π C at z=3π/k have the same velocity 0.5c î. Find the ratio of force magnitudes F₁: F₂.
Options

Question

The magnetic field of an electromagnetic wave is B⃗=B₀(î+ĵ)/√2 cos(kz-ωt). At t=0, charges q₁=4π C at z=π/k and q₂=2π C at z=3π/k have the same velocity 0.5c î. Find the ratio of force magnitudes F₁: F₂.

Options

G1 Physics · Accepted Answer

At both listed z positions the field magnitudes are equal, and the two particles have the same velocity. Thus the force-magnitude factor from E⃗+v⃗×B⃗ is the same; force is proportional to charge. Since q₁:q₂=4π:2π=2:1, F₁:F₂=2:1. Option C.

The magnetic field of an electromagnetic wave is B⃗=B₀(î+ĵ)/√2 cos(kz−ωt). At t=0, charges q₁=4π C at z=π/k and q₂=2π C at z=3π/k have the same velocity 0.5c î. Find the ratio of force magnitudes F₁:F₂.