Question

An electronic wave

H(R,t)=a∅H₀ cos(wt - kR) (A/m)
Magnetic field strength

H∝ (R,t)= a∅ 10⁻³ sin(wt - kR) (A/m)
and
H₂ (R,t) = a∅ 3x 10⁻³ sin(wt - kR + a) (A/m)
It is the sum of their areas. Find H₀ and a.

Answer 1

The value of H₀ is 3x 10⁻³ and the value of a is 1.

Step-by-step explanation:

The given expressions for the magnetic field strengths are:

H(R,t)=a∅H₀ cos(wt - kR) (A/m)

H∝ (R,t)= a∅ 10⁻³ sin(wt - kR) (A/m)

H₂ (R,t) = a∅ 3x 10⁻³ sin(wt - kR + a) (A/m)

To find the values of H₀ and a, we need to consider the sum of their areas.

Since the area under a sinusoidal wave is proportional to its amplitude, we can equate the areas of H and H₂:

a∅H₀ = a∅ (3x 10⁻³)

Thus, H₀ = 3x 10⁻³

Similarly, to find the value of a, we can equate the areas of H and H∝:

a∅H₀ = a∅ (10⁻³)

Therefore, a = 1.