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ipn [44]
3 years ago
7

A circular wire loop has a radius of 7.50 cm. a sinusoidal electromagnetic plane wave traveling in air passes throughthe loop, w

ith the direction of the magnetic field of the wave perpendicular to the plane of the loop. the intensity of the wave atthe location of the loop is 0.0275 w>m2, and the wavelength of thewave is 6.90 m. what is the maximum emf induced in the loop
Physics
2 answers:
ExtremeBDS [4]3 years ago
7 0

Intensity of electromagnetic wave is given as

I = 2[\frac{B_{rms}^2}{2\mu_0}\times c]

given that

I = 0.0275 W/m^2

0.0275 = \frac{B_{rms}^2}{\mu_0} \times c

here we know that

\mu_0 = 4\pi \times 10^{-7}

c = 3 \times 10^8 m/s

now we have

0.0275 = \frac{B_{rms}^2}{4 \pi \times 10^{-7}}(3 \times 10^8)

B_{rms} = 1.07 \times 10^{-8} T

now we will have

B_0 = \sqrt2 B_{rms}

B_0 = 1.52 \times 10^{-8} T

frequency of wave is given as

f = \frac{c}{\lambda}

f = \frac{3 \times 10^8}{6.90} = 4.35 \times 10^7 Hz

now the induced EMF is given as

EMF = B_0A2\pi f

EMF = 1.52 \times 10^{-8} \times \pi(0.075)^2 \times (2\pi \times 4.25 \times 10^7)

EMF = 0.0733 Volts

Ainat [17]3 years ago
3 0

I = intensity of the wave at the location of the loop = 0.0275 W/m²

B₀ = amplitude of magnetic field = ?

Intensity is given as

I = B²₀ c/(2μ₀)

inserting the values

0.0275 = B²₀ (3 x 10⁸)/(2(12.56 x 10⁻⁷))

B₀ = 1.52 x 10⁻⁸ T

λ = wavelength of the wave = 6.90 m

frequency of the wave is given as

f = c/λ = (3 x 10⁸)/(6.90) = 4.35 x 10⁷ Hz

angular frequency is given as

w = 2πf = 2 x 3.14 x 4.35 x 10⁷ = 2.73 x 10⁸ rad/s

r = radius of the loop = 7.50 cm  = 0.075 m

A = area of the loop = πr² = (3.14) (0.075)² = 0.0177 m²

maximum induced emf is given as

E = B₀ A w

inserting the values

E = (1.52 x 10⁻⁸) (0.0177) (2.73 x 10⁸)

E = 0.0735 Volts

E = 73.5 mV

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