Answer:
E₁ = 9.759
sin(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 = 9.759
sin(7.0 × 10⁶ t)