Answer:
1.04 × 10⁻¹⁰ T
Explanation:
Find the speed of the electromagnetic wave
v=c/√k*kw where;
v= is speed of electromagnetic wave
c=speed of light=3×10⁸
k=dielectric constant=3.64
kw=relative permeability =5.8
v= 3.0×10⁸ / √(3.64×5.8)
v=6.91×10⁷ m/s
Find the amplitude of the electromagnetic wave
Bmax=Emax/v where
Bmax is amplitude of electromagnetic wave
Emax is Electric field amplitude
v=speed of electromagnetic wave
Bmax=7.20 × 10⁻³ / 6.91×10⁷ = 1.04 × 10⁻¹⁰ T
1.04 x 10⁻¹⁰ T
Given:
Question:
What is the amplitude of the magnetic field? (in Tesla)
The Process:
Step-1: the speed of propagation of the wave [tex](v)[/tex]
The relationship between [tex]v, c, K, and \ K_m[/tex] can be expressed in the following formula.
[tex]\boxed{ \ v = \frac{c}{\sqrt{K \ K_m}} \ }[/tex]
Let us calculate the speed of propagation of the wave.
[tex]\boxed{ \ v = \frac{3.00 \times 10^8}{\sqrt{(3.64)(5.18)}} \ }[/tex]
We get [tex]\boxed{ \ v = 6.91 \times 10^7 \ m/s \ }[/tex]
Step-2: the amplitude of the magnetic field [tex](B)[/tex]
The magnitude of the relationship between E and B fields is
[tex]\boxed{ \ v = \frac{E_m}{B_m} \ }[/tex]
where,
We set the formula so that the amplitude of the magnetic field becomes the subject.
[tex]\boxed{ \ B_m = \frac{E_m}{v} \ }[/tex]
And now, let us calculate the amplitude of the magnetic field.
[tex]\boxed{ \ B_m = \frac{7.20 \times 10^{-3}}{6.91 \times 10^7} \ }[/tex]
Thus, the amplitude of the magnetic field is [tex]\boxed{ \ B_m = 1.04 \times 10^{-10} \ T \ }[/tex]
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Note-1
What is the wavelength of the wave?
[tex]\boxed{ \ v = \lambda f \ }[/tex]
[tex]\rightarrow \boxed{ \ \lambda = \frac{v}{f} \ } [/tex]
[tex]\boxed{ \ \lambda = \frac{6.91 \times 10^7}{65.0} \ } [/tex]
We get [tex]\boxed{ \ \lambda = 1.06 \times 10^6 \ m/s \ }[/tex]
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Note-2
EM (electromagnetic) wave speed in non-vacuum medium, i.e.,
[tex]\boxed{ \ v = \frac{1}{\sqrt{\epsilon \mu}} \ }[/tex] [tex]\boxed{ \ v = \frac{c}{\sqrt{K \ K_m}} \ }[/tex] [tex]\boxed{ \ v = \frac{c}{n} \ }[/tex] where n is the refraction index.
