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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in simple terms, the principle states that the buoyancy force on an object is equal to the weight of the fluid displaced by the object, or the density of the fluid multiplied by the submerged volume times the gravitational acceleration, g. this is also known as upthrust.