The magnetic field vector of an electromagnetic wave is given by B = B₀(ı̂ + ȷ̂)/(√2)cos(kz - ω t) where ı̂, ȷ̂ represents unit vector along x and y-axis respectively. At t = 0 s, two electric charges q₁ of 4π coulomb and q₂ of 2π coulomb located at (0, 0, π/k) and (0, 0, (3π)/k), respectively, hav…

Question

The magnetic field vector of an electromagnetic wave is given by B = B₀(ı̂ + ȷ̂)/(√2)cos(kz - ω t) where ı̂, ȷ̂ represents unit vector along x and y-axis respectively. At t = 0 s, two electric charges q₁ of 4π coulomb and q₂ of 2π coulomb located at (0, 0, π/k) and (0, 0, (3π)/k), respectively, have the same velocity 0.5c ı̂, (where c is the velocity of light). The ratio of the force acting on charge q₁ to q₂ is

Accepted Answer

(4) 2:1. At t = 0: cos(k · π/k) = cos π = -1 and cos(3π) = -1. So E⃗ and B⃗ are identical at both charges, and both have the same velocity. Force q(E⃗ + v⃗ × B⃗) is then proportional to q. (F₁)/(F₂) = (4π)/(2π) = 2.

Step-by-step solution

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