A radio beacon at rest in deep space emits 16.0 GW of RF power into the blackness. If that power is emitted isotropically, what is the associated magnetic field, at a distance of 150E6 km from the beacon

The associated magnetic field, at a distance of 150E6 km from the beacon is

B = (2.177 × 10⁻¹⁴) T

Explanation:

The intensity of waves, with power P, at a point r, from source is given as

I = (P/A)

The associated electric field for the electromagnetic wave at that point is given as

E = √(2Iμ₀c)

And the associated Magnetic field for the electromagnetic wave is related to the associated electric field through

B = (E/c)

Note that

P = power of the wave = 16.0 GW

= (16 × 10⁹) W

A = Surface area of an imaginary sphere at the point where the intensity of the wave is required = 4πr²

r = distance from the source of the wave to the point where the intensity is required

r = (150 × 10⁶) km = (150 × 10⁹) m

A = 4πr² = 4π × (150 × 10⁹)²

A = (2.827 × 10²³) m²

I = (P/A)

I = (16 × 10⁹) ÷ (2.827 × 10²³)

I = (5.659 × 10⁻¹⁴) W/m²

E = √(2Iμ₀c)

I = intensity of the wave at that point = (5.659 × 10⁻¹⁴) W/m²

μ₀ = magnetic constant or magnetic permeability of vacuum = (4π × 10⁻⁷) H/m

c = speed of light = (3.0 × 10⁸) m/s

E = √(2 × 5.659×10⁻¹⁴ × 4π×10⁻⁷ × 3.0×10⁸)

E = √(4.2668 × 10⁻¹¹)

E = 0.0000065321 N/C

= (6.5321 × 10⁻⁶) N/C

Associated Magnetic field for the electromagnetic wave is related to the associated electric field through

B = (E/c)

E = Electric field = (6.5321 × 10⁻⁶) N/C

c = speed of light = (3.0 × 10⁸) m/s

B = (6.5321 × 10⁻⁶) ÷ (3.0 × 10⁸)

B = (2.177 × 10⁻¹⁴) T

Hope this Helps!!!

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