Three electromagnetic waves arrive at a point from the same direction. they are polarized parallel to an x axis, and their electric fields at the point are e1 = a sin(ωt) for wave 1, e2 = b sin(ωt + φ2) for wave 2, and e3 = c sin(ωt + φ3) for wave 3. here t is time. the constants are a = 3.0 µv/m, b = 4.0 µv/m, c = 5.0 µv/m, ω = 7.0 × 106 rad/s, φ2 = π/4, and φ3 = π/2. what is the amplitude (in µv/m) of the electric field that results from the interference of the three waves?

E₁ = 9.759sin(7.0 × 10⁶ t)

Explanation:

Given:

E₁ = 3sin(7.0 × 10⁶ t)

E₂ = 4sin(7.0 × 10⁶ t + 45°)

E₃ = 5sin(7.0 × 10⁶ t + 90°)

Now,

the net vertical component of Electric field E is

= 3sin(0°) + 4sin(0° + 45°) + 5sin(0° + 90°)

or

= 7.828

Now,

the net horizontal component of Electric field E is

= 3cos(0°) + 4cos(0° + 45°) + 5cos(0° + 90°)

or

= 5.828

Therefore, the resultant Electric field is

or

or

Now, the phase angle is given as:

hence,

E₁ = 9.759sin(7.0 × 10⁶ t)

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