An electromagnetic wave travels in the +x direction and has electric field Eᵧ = 300 sin[ω(t-x / c)] V·m⁻¹. An electron is constrained to move only along the y direction with speed 1.5×10⁶ m·s⁻¹. What is the ratio of the maximum electric-force magnitude to the maximum magnetic-force magnitude on the electron?
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Question

An electromagnetic wave travels in the +x direction and has electric field Eᵧ = 300 sin[ω(t-x / c)] V·m⁻¹. An electron is constrained to move only along the y direction with speed 1.5×10⁶ m·s⁻¹. What is the ratio of the maximum electric-force magnitude to the maximum magnetic-force magnitude on the electron?

Options

G1 Physics · Accepted Answer

For an electromagnetic wave, E(max) ÷ B(max) = c. The maximum electric force on the electron is F(E,max) = eE(max). The maximum magnetic force magnitude is F(B,max) = evB(max), because the electron velocity along y is perpendicular to the magnetic field of the wave. Therefore, F(E,max) ÷ F(B,max) = eE(max) ÷ [evB(max)] = E(max) ÷ [vB(max)] = c ÷ v. Substitute: c = 3×10⁸ m·s⁻¹, v = 1.5×10⁶ m·s⁻¹. Thus, F(E,max) ÷ F(B,max) = 3×10⁸ ÷ 1.5×10⁶ = 200. Correct option: A.